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PROFESSOR: Our last class
Yi is running from his home

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in New Jersey due to snow.

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So he couldn't fly in.

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But actually, now
I'm learning a lot.

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It's a good way to run
the classes going forward.

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I think.

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We may employ it next year.

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So Yi will present CV
modeling for about an hour.

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00:00:55,650 --> 00:01:02,850
And then Jake, Peter and myself,
we will do concluding remarks.

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00:01:02,850 --> 00:01:07,730
We will be happy to answer
any questions on the projects

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00:01:07,730 --> 00:01:09,915
or any questions whatsoever.

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00:01:09,915 --> 00:01:11,420
All Right?

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00:01:11,420 --> 00:01:12,690
So Yi, please.

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Thank you.

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00:01:14,060 --> 00:01:15,550
YI TANG: OK.

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00:01:15,550 --> 00:01:17,590
I'm here.

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00:01:17,590 --> 00:01:19,070
Hi everyone.

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00:01:19,070 --> 00:01:23,300
Sorry I couldn't make it in
person because of the snow.

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00:01:23,300 --> 00:01:28,160
And I'm happy to
have this opportunity

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00:01:28,160 --> 00:01:32,230
to discuss with you
guys counterparty credit

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00:01:32,230 --> 00:01:37,240
risks as a part of our
enterprise-level derivatives

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00:01:37,240 --> 00:01:39,000
modeling.

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00:01:39,000 --> 00:01:42,970
I run a Cross Asset Modeling
Group at Morgan Stanley.

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00:01:42,970 --> 00:01:44,940
And hopefully you
will see why it's

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00:01:44,940 --> 00:01:46,350
called Cross Asset Modeling.

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00:01:50,980 --> 00:01:54,190
OK, counterparty credit
risk exists mainly

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00:01:54,190 --> 00:01:57,600
in OTC derivatives.

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00:01:57,600 --> 00:02:00,580
We have an OTC derivative trade.

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00:02:00,580 --> 00:02:04,350
Sometimes you owe your
counterparty money.

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00:02:04,350 --> 00:02:08,850
Sometimes your counterparty
owes you money.

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00:02:08,850 --> 00:02:14,090
If your counterparty owes you
money, on the payment date,

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00:02:14,090 --> 00:02:17,630
your counterparty
may actually default,

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00:02:17,630 --> 00:02:20,440
and therefore, either
will not pay you

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00:02:20,440 --> 00:02:24,150
the full amount it owes you.

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00:02:24,150 --> 00:02:28,270
The default event includes
bankruptcy, failure to pay

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00:02:28,270 --> 00:02:30,520
and a few other events.

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00:02:30,520 --> 00:02:34,310
So obviously, we
have a default risk.

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00:02:34,310 --> 00:02:37,810
If our counterparty
defaults, we would

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00:02:37,810 --> 00:02:42,320
lose part of our receivable.

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00:02:42,320 --> 00:02:46,580
However, the question is before
the counterparty defaults,

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00:02:46,580 --> 00:02:48,970
do have any other risks?

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00:02:48,970 --> 00:02:52,800
Imagine you have a case where
your counterparty will pay you

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00:02:52,800 --> 00:02:55,920
in 10 years.

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00:02:55,920 --> 00:02:59,010
So he doesn't need
to pay you anything.

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00:02:59,010 --> 00:03:01,240
Then the question
is are you concerned

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00:03:01,240 --> 00:03:05,440
about counterparty risks or not?

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00:03:05,440 --> 00:03:10,330
Well, the question is yes,
as many of you probably know,

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00:03:10,330 --> 00:03:14,550
it's the mark-to-market
risk due to the likelihood

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of a counterparty
future default.

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00:03:19,450 --> 00:03:23,190
It is like the
counterparty spike widens,

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00:03:23,190 --> 00:03:25,700
even though you do not need a
payment from you counterparty.

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00:03:28,340 --> 00:03:32,580
If you were to sell,
a derivative trade

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00:03:32,580 --> 00:03:37,120
to someone, then someone may
actually worry about that.

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00:03:37,120 --> 00:03:39,380
So therefore the
mark-to-market will

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become lower if the
counterparty is spread wider.

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00:03:47,383 --> 00:03:53,410
This is similar to a corporate
bond in terms of economics.

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You own a bond on the
coupon payments date,

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00:03:57,140 --> 00:04:00,820
or on the principal date,
the counterparty can default.

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Of course, they can
default in between also.

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00:04:03,800 --> 00:04:05,620
But in terms of
terminology, this

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00:04:05,620 --> 00:04:08,310
is not called counterparty risk.

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00:04:08,310 --> 00:04:10,080
This is called issue risk.

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00:04:13,730 --> 00:04:18,579
So here comes the important
concept credit valuation

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adjustment.

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As we know the
counterparty is a risk.

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Whenever there's a risk, we
could put a price on that risk.

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Credit valuation
adjustment, CVA,

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00:04:33,590 --> 00:04:38,690
essentially is the price of
a counterparty credit risk.

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00:04:38,690 --> 00:04:40,940
Mainly mark-to-market
risks, of course,

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include default risk too.

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00:04:43,820 --> 00:04:49,100
It is an adjustment to the
price of mark-to-market

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00:04:49,100 --> 00:04:54,830
from a counterparty-default-free
model, the broker quote.

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00:04:57,360 --> 00:05:01,490
So people know,
there's a broker quote.

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00:05:01,490 --> 00:05:05,990
The broker doesn't know
the counterparty risk.

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00:05:05,990 --> 00:05:11,760
A lot of our trade models do
not know the counterparty risk

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00:05:11,760 --> 00:05:17,050
either, mainly because
of we're holding it back,

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which I will talk
about in a minute.

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00:05:21,200 --> 00:05:24,980
Therefore, there is
a need to actually

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00:05:24,980 --> 00:05:29,640
have a separate
price of CVA to be

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00:05:29,640 --> 00:05:33,680
added to the price
for mark-to-market

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00:05:33,680 --> 00:05:36,070
from counterparty
default free model

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00:05:36,070 --> 00:05:40,220
to get a true economic price.

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00:05:40,220 --> 00:05:43,340
In contrast, in terms of
a bond, typically there's

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00:05:43,340 --> 00:05:49,520
no need for CVA because it is
priced in the market already.

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00:05:52,340 --> 00:05:58,370
And CVA not only has important
mark-to-market implications,

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00:05:58,370 --> 00:06:03,880
it is also a part of
our Basel III capital.

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00:06:03,880 --> 00:06:08,840
Not only change your valuation,
but could impact your return

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00:06:08,840 --> 00:06:09,930
on capital.

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00:06:09,930 --> 00:06:13,070
Because of a CVA risk,
the capital requirements

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00:06:13,070 --> 00:06:15,530
typically is higher.

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00:06:15,530 --> 00:06:22,750
So you may have a bigger
denominator in this return RE,

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00:06:22,750 --> 00:06:27,170
return on capital
or return on equity.

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00:06:27,170 --> 00:06:32,120
CVA risk, as you may know, has
been a very important risk,

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00:06:32,120 --> 00:06:36,860
especially since
the crisis in 2008.

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During the crisis, a significant
financial loss actually

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00:06:40,790 --> 00:06:46,270
is coming from CVA loss,
meaning mark-to-market loss

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00:06:46,270 --> 00:06:49,060
due to counterparties'
future default.

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00:06:49,060 --> 00:06:51,600
And this loss turned
out to be actually

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higher than the
actual default loss

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00:06:54,700 --> 00:07:01,600
than the actual
counterparty default.

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00:07:01,600 --> 00:07:04,120
Again, coming back
to our question,

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00:07:04,120 --> 00:07:07,720
how do we think in terms
of pricing a derivatives

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00:07:07,720 --> 00:07:14,330
and price the CVA together
with the derivatives.

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00:07:14,330 --> 00:07:17,950
First of all, it adds
some portfolio effect

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00:07:17,950 --> 00:07:20,460
the counterparty can
trade multiple trades.

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00:07:20,460 --> 00:07:22,540
And the default
loss or default risk

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00:07:22,540 --> 00:07:25,330
can be different depending
on the portfolio.

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00:07:25,330 --> 00:07:29,790
And when people use a
trade-level derivatives model,

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00:07:29,790 --> 00:07:34,150
which is by default what people
would call a derivatives model,

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00:07:34,150 --> 00:07:38,690
typically you price each
trade, price one trade at time.

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00:07:38,690 --> 00:07:42,380
And then you aggregate the
mark-to-market together

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00:07:42,380 --> 00:07:44,550
to get a portfolio valuation.

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00:07:44,550 --> 00:07:47,720
So when you price
one trade, you do not

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00:07:47,720 --> 00:07:50,360
need to know there may
be another trade facing

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00:07:50,360 --> 00:07:51,700
the same counterparty.

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00:07:51,700 --> 00:07:56,450
But for CVA or counterparty
risk, this is not true.

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00:07:56,450 --> 00:07:58,250
We'll go over some
examples soon.

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00:08:02,070 --> 00:08:04,690
This is the one
application of what

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00:08:04,690 --> 00:08:07,390
I call enterprise-level
derivatives,

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00:08:07,390 --> 00:08:12,100
essentially focusing on
modeling the non-linear effects,

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00:08:12,100 --> 00:08:15,815
non-linear risks in a
derivatives portfolio.

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00:08:18,569 --> 00:08:19,735
Here's a couple of examples.

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00:08:19,735 --> 00:08:24,120
Hopefully, it will help you
guys to gain some intuition

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00:08:24,120 --> 00:08:28,310
on the counterparty
risks and CVA.

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00:08:28,310 --> 00:08:32,440
Suppose you have an OTC
derivatives trade, for instance

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00:08:32,440 --> 00:08:34,820
like an IR swap.

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00:08:34,820 --> 00:08:38,130
It could be a
portfolio of trades.

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00:08:38,130 --> 00:08:39,870
Let's make it simple.

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00:08:39,870 --> 00:08:45,530
Let's assume the trade
PV was 0 on day one.

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00:08:45,530 --> 00:08:48,890
Of course, we assume
we don't know anything

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00:08:48,890 --> 00:08:51,090
about the counterparty
credit risk.

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00:08:51,090 --> 00:08:54,140
We don't know
anything about CVA.

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00:08:54,140 --> 00:09:00,260
This is just to show how
CVA is recognized by people.

141
00:09:00,260 --> 00:09:04,340
So to start with
again, the trade PV

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00:09:04,340 --> 00:09:10,640
was 0 on day one, which is
true for a lot of co-op trades.

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00:09:10,640 --> 00:09:18,020
And then the trade PV became
$100 million dollars later on.

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00:09:18,020 --> 00:09:25,440
And then your counterparty
defaults with 50% recovery.

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00:09:25,440 --> 00:09:30,755
And you'll get paid
$50 million of cash.

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00:09:33,470 --> 00:09:37,350
OK, so $100 million
times 50% recovery.

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00:09:37,350 --> 00:09:39,150
If the counterparty
doesn't default,

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00:09:39,150 --> 00:09:42,100
you eventually would
get $100 million.

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00:09:42,100 --> 00:09:47,720
Now he defaults, you get
half of it, $50 million.

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00:09:47,720 --> 00:09:53,600
The question is have you
made $50 million dollars

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00:09:53,600 --> 00:09:59,320
or have you lost $50 million
over the life of the trade.

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00:10:03,070 --> 00:10:05,740
Anyone have any ideas?

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00:10:05,740 --> 00:10:07,820
Can people raise your
hand if you think

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00:10:07,820 --> 00:10:09,170
you have made $50 million?

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00:10:13,114 --> 00:10:14,900
Can I see the
people in the class?

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00:10:14,900 --> 00:10:16,270
I couldn't see anyone.

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00:10:19,054 --> 00:10:22,440
PROFESSOR: How do I raise this?

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00:10:22,440 --> 00:10:25,240
YI TANG: OK, no one thinks
you made the $50 million.

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00:10:25,240 --> 00:10:28,250
So I guess then,
did you all think

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00:10:28,250 --> 00:10:29,805
you have lost $50 million?

161
00:10:32,354 --> 00:10:34,020
Can people raise their
hand if you think

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00:10:34,020 --> 00:10:35,440
you have lost $50 million?

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00:10:38,800 --> 00:10:40,930
OK, I see people.

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00:10:40,930 --> 00:10:42,430
Some people did not
raise your hand.

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00:10:42,430 --> 00:10:44,440
That means you are
thinking you are flat?

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00:10:46,990 --> 00:10:51,440
Or maybe you want to
save your opinion later?

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00:10:51,440 --> 00:10:56,620
OK, so this is a common
question I normally

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00:10:56,620 --> 00:10:59,020
ask in my presentation.

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00:10:59,020 --> 00:11:01,270
And I typically get two answers.

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00:11:01,270 --> 00:11:05,770
Some people think
they've made $50 million.

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00:11:05,770 --> 00:11:09,390
Some people think
they've lost $50 million.

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00:11:09,390 --> 00:11:15,610
And there was one case, someone
said OK, you know they're flat.

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00:11:18,220 --> 00:11:20,990
Now, this would look like
a new interesting situation

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00:11:20,990 --> 00:11:24,260
where no one thinks
you made $50 million.

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00:11:24,260 --> 00:11:30,550
I mean, come on, you have $50
million of cash in the door.

176
00:11:30,550 --> 00:11:34,480
And they don't think you
have made $50 million.

177
00:11:34,480 --> 00:11:36,500
You have a $0 from day one.

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00:11:36,500 --> 00:11:37,750
Now, you have $50 million.

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00:11:41,433 --> 00:11:43,830
OK?

180
00:11:43,830 --> 00:11:46,640
All right, anyway
so for those of you

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00:11:46,640 --> 00:11:48,806
who think you have lost
money-- I don't know if it's

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00:11:48,806 --> 00:11:53,440
a good idea [? Ronny-- ?]
can someone tell us why do

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00:11:53,440 --> 00:11:55,740
you think you lost $50 million?

184
00:11:55,740 --> 00:11:58,810
You went from 0 to
positive $50 million.

185
00:11:58,810 --> 00:12:00,720
Why do you think you
lost $50 million?

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00:12:06,650 --> 00:12:09,165
Are we equipped to allow
people to answer questions?

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00:12:12,886 --> 00:12:15,760
PROFESSOR: Yeah, I think
if someone presses a button

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00:12:15,760 --> 00:12:16,840
in front of them.

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00:12:19,920 --> 00:12:25,556
YI TANG: OK, so people choose
not to voice your opinion?

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00:12:25,556 --> 00:12:28,210
AUDIENCE: It is because
you have to pay to swap

191
00:12:28,210 --> 00:12:30,060
and you have to pay
$100 million to someone

192
00:12:30,060 --> 00:12:32,850
on the other side of trade?

193
00:12:32,850 --> 00:12:34,100
YI TANG: OK, very good.

194
00:12:34,100 --> 00:12:36,520
So essentially, you
are saying hedging.

195
00:12:36,520 --> 00:12:39,380
That was what you
are trying to get to?

196
00:12:39,380 --> 00:12:42,810
So you have a swap
as 0 and you have

197
00:12:42,810 --> 00:12:45,326
an offsetting swap as a hedge.

198
00:12:45,326 --> 00:12:47,269
Is that what you
are trying to say?

199
00:12:47,269 --> 00:12:47,810
AUDIENCE: No.

200
00:12:47,810 --> 00:12:50,780
I'm saying that if you're
the intermediary for a swap,

201
00:12:50,780 --> 00:12:52,990
then you have to pay $100
million on the other end.

202
00:12:52,990 --> 00:12:56,715
So if you're receiving 50 and
paying 100, you have a loss.

203
00:12:56,715 --> 00:12:57,590
YI TANG: That's good.

204
00:12:57,590 --> 00:12:58,930
Right, so intermediary is right.

205
00:12:58,930 --> 00:13:03,060
And that's similar to
a hedge situation also.

206
00:13:03,060 --> 00:13:04,340
So that's correct.

207
00:13:04,340 --> 00:13:09,060
That's the basically
the reason for a dealer.

208
00:13:09,060 --> 00:13:11,330
Essentially, we are
required to hedge.

209
00:13:11,330 --> 00:13:13,640
We're very tight on the limit.

210
00:13:13,640 --> 00:13:15,740
We actually would
lose $50 million

211
00:13:15,740 --> 00:13:19,770
maybe on the hedge fund.

212
00:13:19,770 --> 00:13:24,910
When our trade went from 0
to a positive $100 million,

213
00:13:24,910 --> 00:13:30,760
our hedge would have gone from
to 0 to negative $100 million.

214
00:13:30,760 --> 00:13:38,650
In fact, we receive only half
of what we need to receive.

215
00:13:38,650 --> 00:13:42,390
And yet, we have to pay
the full amount that we

216
00:13:42,390 --> 00:13:44,860
need to pay on the hedge side.

217
00:13:44,860 --> 00:13:48,900
Essentially, we
lost $50 million.

218
00:13:48,900 --> 00:13:53,590
But that's where the CVA
and CV trading, CV risk

219
00:13:53,590 --> 00:13:55,430
management would come in.

220
00:13:55,430 --> 00:14:00,460
Again, CVA is the price of
a counterparty credit risk.

221
00:14:00,460 --> 00:14:04,420
And you know, if you hedge,
the underlying trader

222
00:14:04,420 --> 00:14:08,500
or whoever trades swap, if
you hedge with the CV desk.

223
00:14:08,500 --> 00:14:13,130
Theoretically, you
will be made whole

224
00:14:13,130 --> 00:14:18,043
on a counterparty default. So
you would receive $50 million

225
00:14:18,043 --> 00:14:20,750
from counterparty,
and theoretically you

226
00:14:20,750 --> 00:14:24,110
receive $50 million
from the CV's desk

227
00:14:24,110 --> 00:14:26,314
if you hedge with CV desk.

228
00:14:29,150 --> 00:14:34,050
Now, the second part is
how do we quantify CVA.

229
00:14:34,050 --> 00:14:37,038
How much is the CVA?

230
00:14:37,038 --> 00:14:39,320
CV on the receivable,
which we typically

231
00:14:39,320 --> 00:14:42,100
charge to the
counterparty, essentially

232
00:14:42,100 --> 00:14:45,740
is given by this formula.

233
00:14:45,740 --> 00:14:49,010
MPE means mean
positive exposure,

234
00:14:49,010 --> 00:14:52,150
meaning only our receivable
sides when the counterparty

235
00:14:52,150 --> 00:14:55,660
owes us money, and times
the counterparty CDS par

236
00:14:55,660 --> 00:15:00,480
spread, times duration.

237
00:15:00,480 --> 00:15:02,880
The wider the spread
the more likely

238
00:15:02,880 --> 00:15:07,200
the counterparty will
default, the more we

239
00:15:07,200 --> 00:15:09,290
need to charge on the CVA.

240
00:15:09,290 --> 00:15:11,870
And the same thing is
true for the duration.

241
00:15:11,870 --> 00:15:13,790
The longer the
duration of trade is,

242
00:15:13,790 --> 00:15:16,490
there's more time
for the counterparty

243
00:15:16,490 --> 00:15:18,480
to default so we charge more.

244
00:15:18,480 --> 00:15:21,800
Very importantly,
there's a negative sign.

245
00:15:21,800 --> 00:15:26,890
Because CVA on the receivable
side, is our liability.

246
00:15:26,890 --> 00:15:30,890
It's what we charge
our counterparty.

247
00:15:30,890 --> 00:15:33,230
And there are some
theoretical articles,

248
00:15:33,230 --> 00:15:35,350
they don't include
the sign, that's

249
00:15:35,350 --> 00:15:37,720
OK for theoretical purposes.

250
00:15:37,720 --> 00:15:40,810
But practically, if
you miss the sign

251
00:15:40,810 --> 00:15:42,333
things will get very confusing.

252
00:15:45,590 --> 00:15:49,095
Now, here is more
accurate formula for CVA.

253
00:15:49,095 --> 00:15:53,670
You know how the MPE
side, on the asset side.

254
00:15:53,670 --> 00:15:57,320
So we can see to start
with, there's an indicator

255
00:15:57,320 --> 00:16:02,040
function where this capital T is
the final maturity of the trade

256
00:16:02,040 --> 00:16:04,260
or counterparty portfolio.

257
00:16:04,260 --> 00:16:11,160
This tau is the counterparty's
default time, first default

258
00:16:11,160 --> 00:16:13,170
time.

259
00:16:13,170 --> 00:16:21,540
And if the tau is greater
than this capital T,

260
00:16:21,540 --> 00:16:23,490
essentially that means
a default happens

261
00:16:23,490 --> 00:16:26,940
after the counterparty
portfolio matures.

262
00:16:26,940 --> 00:16:29,690
And therefore, we don't
have counterparty risk.

263
00:16:29,690 --> 00:16:32,660
So that's what this
indicator is about.

264
00:16:32,660 --> 00:16:36,670
If the counterparty defaults
before the maturity,

265
00:16:36,670 --> 00:16:41,100
that's when we will have
counterparty credit risk.

266
00:16:41,100 --> 00:16:48,410
And there's a future evaluation
of the counterparty portfolio

267
00:16:48,410 --> 00:16:50,680
right before the
counterparty default.

268
00:16:50,680 --> 00:16:55,710
And this is how much collateral
we hold against this portfolio.

269
00:16:55,710 --> 00:17:01,200
So the net receivable,
the net amount,

270
00:17:01,200 --> 00:17:05,849
where the future value is
greater than the collateral,

271
00:17:05,849 --> 00:17:10,770
is our sort of
exposure, how much

272
00:17:10,770 --> 00:17:13,780
the counterparty would owe us.

273
00:17:13,780 --> 00:17:17,540
And this 1 minus R essentially
is the discount rate.

274
00:17:17,540 --> 00:17:21,880
So 1 minus R times the
exposure essentially

275
00:17:21,880 --> 00:17:25,790
is the future loss
given default.

276
00:17:25,790 --> 00:17:30,170
And beta essentially is a
normal mock money market

277
00:17:30,170 --> 00:17:33,700
account for defaulting,
and this is the expectation

278
00:17:33,700 --> 00:17:37,440
in the risk-neutral measure.

279
00:17:37,440 --> 00:17:38,835
It looks simple.

280
00:17:38,835 --> 00:17:44,220
But if you get to the details,
it's actually very complex

281
00:17:44,220 --> 00:17:46,595
maybe because the
portfolio effect

282
00:17:46,595 --> 00:17:50,030
and this option-like payoff.

283
00:17:50,030 --> 00:17:53,470
If you recognize this
positive sign here,

284
00:17:53,470 --> 00:17:55,740
essentially you recognize
this is like options.

285
00:17:59,080 --> 00:18:05,034
And so again, here is about some
details of non-linear portfolio

286
00:18:05,034 --> 00:18:06,690
effects.

287
00:18:06,690 --> 00:18:09,940
First of all, we talk
about offsetting trades.

288
00:18:09,940 --> 00:18:15,155
In the previous example,
you have one trade

289
00:18:15,155 --> 00:18:17,410
and went from 0 to $100 million.

290
00:18:17,410 --> 00:18:20,560
Counterparty defaults, you get
paid $50 million, essentially,

291
00:18:20,560 --> 00:18:22,670
you lost $50 million.

292
00:18:22,670 --> 00:18:24,850
But what if you have
another trade facing

293
00:18:24,850 --> 00:18:26,200
the same counterparty?

294
00:18:26,200 --> 00:18:29,080
Well, that's offsetting.

295
00:18:29,080 --> 00:18:32,490
When the first trade went
from 0 to $100 million,

296
00:18:32,490 --> 00:18:37,620
the offsetting trade can go
from 0 to negative $100 million.

297
00:18:37,620 --> 00:18:40,560
And therefore if the
counterparty were to default,

298
00:18:40,560 --> 00:18:42,230
you're going to have
a 0 default loss.

299
00:18:44,850 --> 00:18:47,740
That's just one example
of portfolio effects

300
00:18:47,740 --> 00:18:49,450
because I'm offsetting trades.

301
00:18:49,450 --> 00:18:52,370
So therefore, in
order to price CVA,

302
00:18:52,370 --> 00:18:55,970
you've got to know all
the trades you have

303
00:18:55,970 --> 00:18:58,860
facing the same counterparty.

304
00:18:58,860 --> 00:19:01,630
This is very different
from a trade-level model

305
00:19:01,630 --> 00:19:04,460
where you only need to
know one trade at a time.

306
00:19:06,990 --> 00:19:10,840
There's also
asymmetry of handling

307
00:19:10,840 --> 00:19:16,350
of the receivable, meaning
assets versus the payable,

308
00:19:16,350 --> 00:19:19,360
meaning liabilities.

309
00:19:19,360 --> 00:19:27,100
And that's where the
option-like payoff comes about.

310
00:19:27,100 --> 00:19:30,810
Typically, roughly
speaking, if we

311
00:19:30,810 --> 00:19:34,290
have a receivable
from our counterparty,

312
00:19:34,290 --> 00:19:36,900
if the counterparty
were to default we're

313
00:19:36,900 --> 00:19:39,680
going to receive
a fraction of it.

314
00:19:39,680 --> 00:19:44,100
So we would incur default loss.

315
00:19:44,100 --> 00:19:48,880
However, if we have a
payable to our counterparty,

316
00:19:48,880 --> 00:19:53,165
if the counterparty
were to default,

317
00:19:53,165 --> 00:19:56,250
we more or less need
to pay the full amount.

318
00:19:56,250 --> 00:19:58,930
We don't have a
default gain, per se.

319
00:19:58,930 --> 00:20:04,140
So this asymmetry is the reason
for this option-like payoff

320
00:20:04,140 --> 00:20:08,290
we just saw previously.

321
00:20:08,290 --> 00:20:11,530
And as you know,
a counterparty can

322
00:20:11,530 --> 00:20:14,850
trade many derivative
instruments

323
00:20:14,850 --> 00:20:19,340
across many assets, such as
interest rate, FX, credit,

324
00:20:19,340 --> 00:20:23,040
equities, a lot of
time also commodities

325
00:20:23,040 --> 00:20:27,110
and sometimes also mortgage.

326
00:20:27,110 --> 00:20:30,330
And then my group is
responsible for the modeling

327
00:20:30,330 --> 00:20:34,775
of the underlying
exposure for CVA

328
00:20:34,775 --> 00:20:38,280
for capital as well
as for liquidity,

329
00:20:38,280 --> 00:20:40,960
because multiple
assets are involved

330
00:20:40,960 --> 00:20:43,950
and we need to
model cross assets.

331
00:20:43,950 --> 00:20:49,980
So therefore, we named our
group Cross Asset Modeling.

332
00:20:49,980 --> 00:20:54,300
Furthermore, it is not only we
have option-like payoff, which

333
00:20:54,300 --> 00:20:57,840
is non-linear, we have
an option essentially

334
00:20:57,840 --> 00:21:02,710
on a basket of a cross
asset derivative trades.

335
00:21:02,710 --> 00:21:08,980
And the modeling becomes
even more difficult.

336
00:21:08,980 --> 00:21:23,120
So that's when the
enterprise-level will come in.

337
00:21:23,120 --> 00:21:25,970
And the enterprise-level
model, which

338
00:21:25,970 --> 00:21:29,260
we'll touch upon
even more later on,

339
00:21:29,260 --> 00:21:34,450
will need to leverage
trade-level derivative models,

340
00:21:34,450 --> 00:21:36,090
and therefore, will
need to do a lot

341
00:21:36,090 --> 00:21:40,850
of martingale-related
stuff, martingale testing,

342
00:21:40,850 --> 00:21:45,040
resampling, interpolation.

343
00:21:45,040 --> 00:21:48,320
So here's a little bit more
information on the CVA.

344
00:21:48,320 --> 00:21:52,900
We have talked about
assets or MPE CVA,

345
00:21:52,900 --> 00:21:56,360
essentially for our
assets or receivable.

346
00:21:56,360 --> 00:21:59,940
In this formula, we
have discussed already

347
00:21:59,940 --> 00:22:00,610
the first one.

348
00:22:03,370 --> 00:22:10,380
There is also, theoretically,
a liability CVA.

349
00:22:10,380 --> 00:22:17,070
Essentially, it is the CV
on the payable side, when

350
00:22:17,070 --> 00:22:27,930
the bank or when us having
a likelihood of default.

351
00:22:27,930 --> 00:22:32,300
And this is a benefit
for us, all right.

352
00:22:32,300 --> 00:22:35,402
So the formula is
fairly symmetric, as you

353
00:22:35,402 --> 00:22:40,170
can recognize, except the
default time or default

354
00:22:40,170 --> 00:22:45,550
event is not for the
counterparty but for us.

355
00:22:45,550 --> 00:22:46,490
OK?

356
00:22:46,490 --> 00:22:52,000
And then the positive sign
here became negative sign,

357
00:22:52,000 --> 00:22:56,817
essential to indicate this is
a payable negative liability

358
00:22:56,817 --> 00:22:57,317
to us.

359
00:23:01,660 --> 00:23:06,440
This is an interesting
discussion first to default.

360
00:23:06,440 --> 00:23:12,300
We talked about how if the
counterparty were to default,

361
00:23:12,300 --> 00:23:19,120
we more or less pay the
counterparty full amount.

362
00:23:19,120 --> 00:23:23,230
So argument can be used
on the receivable side.

363
00:23:23,230 --> 00:23:30,480
So if we have a receivable, and
if we were to default first,

364
00:23:30,480 --> 00:23:32,670
roughly speaking
the counterparty

365
00:23:32,670 --> 00:23:37,830
would pay us close
to the full amount.

366
00:23:37,830 --> 00:23:40,575
And there, some people start
to think about OK, when

367
00:23:40,575 --> 00:23:44,740
we price CVA, we've got to
know, among counterparty

368
00:23:44,740 --> 00:23:49,800
and ourselves, which
one is first to default.

369
00:23:49,800 --> 00:23:55,920
But my argument is that we
do not need to consider that.

370
00:23:55,920 --> 00:23:57,960
And I have some
reference for you guys

371
00:23:57,960 --> 00:24:03,320
to take a look if you are
interested in this topic,

372
00:24:03,320 --> 00:24:06,220
but I'm not going to
spend much time because we

373
00:24:06,220 --> 00:24:07,715
have lots to go over.

374
00:24:10,340 --> 00:24:13,950
Now, here's another example.

375
00:24:13,950 --> 00:24:19,090
You have a trade, same
as the previous trade.

376
00:24:19,090 --> 00:24:23,440
The trade PV was 0 on
day one, and the trade PV

377
00:24:23,440 --> 00:24:28,100
becomes $100 million later on.

378
00:24:28,100 --> 00:24:31,526
This time of course
the counterparty risk

379
00:24:31,526 --> 00:24:34,992
are properly hedged.

380
00:24:34,992 --> 00:24:40,410
Then the question is do
you have any other risks.

381
00:24:45,503 --> 00:24:49,340
Does anyone want to try to tell
us do you see any other risks?

382
00:25:03,340 --> 00:25:07,480
There are actually
several categories of risk

383
00:25:07,480 --> 00:25:08,580
we will have.

384
00:25:08,580 --> 00:25:12,610
I wonder if anyone
would like to try

385
00:25:12,610 --> 00:25:14,420
to share with us your opinion.

386
00:25:16,960 --> 00:25:18,370
Sorry, I couldn't hear you.

387
00:25:18,370 --> 00:25:20,730
Yes?

388
00:25:20,730 --> 00:25:23,257
AUDIENCE: Some form
of interest rate risk.

389
00:25:23,257 --> 00:25:24,840
YI TANG: Interest
rate risk, OK, fine.

390
00:25:24,840 --> 00:25:26,340
OK fine, this is a market risk.

391
00:25:26,340 --> 00:25:29,570
Yes, you're right there
is interest rate risk,

392
00:25:29,570 --> 00:25:33,260
but I did mention here that
the market risks are properly

393
00:25:33,260 --> 00:25:34,870
hedged.

394
00:25:34,870 --> 00:25:37,860
So that means this interest
rate risk of the trade

395
00:25:37,860 --> 00:25:40,250
will be handled by the hedge.

396
00:25:40,250 --> 00:25:41,132
What other risks?

397
00:25:41,132 --> 00:25:42,590
AUDIENCE: Is there
a key man risks?

398
00:25:42,590 --> 00:25:45,390
So if the trader that made
the trade leaves and doesn't

399
00:25:45,390 --> 00:25:46,280
know about the--

400
00:25:46,280 --> 00:25:46,905
YI TANG: Ah, OK

401
00:25:46,905 --> 00:25:48,760
AUDIENCE: --portfolio?

402
00:25:48,760 --> 00:25:50,180
YI TANG: That's a good point.

403
00:25:50,180 --> 00:25:52,340
Yeah, there is a risk like that.

404
00:25:52,340 --> 00:25:53,690
Yeah.

405
00:25:53,690 --> 00:25:54,600
Any other risks?

406
00:25:59,931 --> 00:26:00,430
OK.

407
00:26:03,340 --> 00:26:04,760
Let's go over this then.

408
00:26:07,840 --> 00:26:14,800
I claim there is a cash
flow liquidity funding risk.

409
00:26:14,800 --> 00:26:16,930
OK?

410
00:26:16,930 --> 00:26:19,475
Our trade is not collateralized.

411
00:26:22,180 --> 00:26:29,080
And then I claim we need funding
for uncollateralized derivative

412
00:26:29,080 --> 00:26:35,840
receivables, meaning we are
about to receive $100 million

413
00:26:35,840 --> 00:26:37,040
in the future.

414
00:26:37,040 --> 00:26:40,170
We don't have it now.

415
00:26:40,170 --> 00:26:47,540
And I claim we actually need
to come up with cash for it

416
00:26:47,540 --> 00:26:49,945
in many cases, in most
cases, not every trade.

417
00:26:56,250 --> 00:27:00,070
Anyone have any idea of why when
you are about to receive money,

418
00:27:00,070 --> 00:27:01,855
you actually need to
come up with money?

419
00:27:08,014 --> 00:27:13,270
This comes back to the hedge
argument similar to CVA.

420
00:27:13,270 --> 00:27:17,605
Essentially, if you
were to hedge your trade

421
00:27:17,605 --> 00:27:20,877
with futures or
with another dealer

422
00:27:20,877 --> 00:27:23,750
which are typically
collateralized.

423
00:27:23,750 --> 00:27:27,500
That means when you are about
to receive $100 million,

424
00:27:27,500 --> 00:27:32,750
essentially you are about to
pay $30 million on your hedge.

425
00:27:32,750 --> 00:27:37,060
In fact, you had to be futures
that maybe mark to market, that

426
00:27:37,060 --> 00:27:39,720
means you need to
actually really come up

427
00:27:39,720 --> 00:27:42,170
with $100 million cash.

428
00:27:42,170 --> 00:27:46,140
The same is true for
collateralized trades.

429
00:27:46,140 --> 00:27:49,390
And there that's
where the risk is.

430
00:27:49,390 --> 00:27:51,890
Because when you need to
come up with this money

431
00:27:51,890 --> 00:27:56,210
and you don't have it,
what are you going to do?

432
00:27:56,210 --> 00:27:58,080
You may end up like Lehman.

433
00:28:01,700 --> 00:28:04,330
And there's also a
contingent on the liquidity

434
00:28:04,330 --> 00:28:09,650
risk, meaning how much liquidity
risk is dependent on the market

435
00:28:09,650 --> 00:28:12,810
conditions, how much
interest rates changed,

436
00:28:12,810 --> 00:28:16,585
how much other market risk
factor changes like that.

437
00:28:19,440 --> 00:28:22,132
And depending on the
market condition,

438
00:28:22,132 --> 00:28:25,290
the liquidity may
be quite different

439
00:28:25,290 --> 00:28:27,050
and you may not know beforehand.

440
00:28:27,050 --> 00:28:29,220
So that's the another challenge.

441
00:28:29,220 --> 00:28:34,630
[INAUDIBLE] If you turn
the argument around,

442
00:28:34,630 --> 00:28:38,590
applying the argument
to the payable

443
00:28:38,590 --> 00:28:41,240
and if you have
uncollateralized payable,

444
00:28:41,240 --> 00:28:45,130
essentially you would have a
funding or liquidity benefit.

445
00:28:45,130 --> 00:28:48,490
So one interesting thing to
manage this liquidity risk

446
00:28:48,490 --> 00:28:54,240
essentially is to use
uncollateralized payable

447
00:28:54,240 --> 00:28:58,330
funding benefits
to partially hedge

448
00:28:58,330 --> 00:29:01,260
the funding risk in
uncollateralized derivatives

449
00:29:01,260 --> 00:29:02,670
receivables.

450
00:29:02,670 --> 00:29:07,510
There are a lot of other
risks, for instance, tail risk

451
00:29:07,510 --> 00:29:09,710
and equity capital risks.

452
00:29:15,150 --> 00:29:20,330
Now here is one more example I'd
like to go over with you guys

453
00:29:20,330 --> 00:29:24,270
on the application of CVA.

454
00:29:24,270 --> 00:29:29,190
This is about studying put
options or put spreads.

455
00:29:29,190 --> 00:29:32,720
If you trade stocks
yourself, you

456
00:29:32,720 --> 00:29:34,240
may have thought
about this problem.

457
00:29:34,240 --> 00:29:38,550
I mean, either you can
buy the stock outright

458
00:29:38,550 --> 00:29:44,682
or you sell put possibly
with a strike lower

459
00:29:44,682 --> 00:29:45,640
than the current price.

460
00:29:48,770 --> 00:29:54,290
With that, you more or
less have a similar payout.

461
00:29:54,290 --> 00:29:56,340
Some people may
argue OK, if you see

462
00:29:56,340 --> 00:30:00,290
put, if your stock comes down,
you're going to lose money.

463
00:30:00,290 --> 00:30:02,970
But you're going to lose
money if you were to hold

464
00:30:02,970 --> 00:30:06,590
the stock outright also.

465
00:30:06,590 --> 00:30:08,750
One of these strategies
that if you sell

466
00:30:08,750 --> 00:30:11,250
put, if the stock
is not put to you,

467
00:30:11,250 --> 00:30:15,410
and you're not participating
the up side when the stock

468
00:30:15,410 --> 00:30:18,970
price increases significantly
then you are not

469
00:30:18,970 --> 00:30:21,690
going to capture that price.

470
00:30:21,690 --> 00:30:23,570
But of course, one
thing people can do

471
00:30:23,570 --> 00:30:25,730
is [? you continue to ?]
sell put so they

472
00:30:25,730 --> 00:30:29,790
become like an income trade.

473
00:30:29,790 --> 00:30:31,300
So it's an interesting strategy.

474
00:30:31,300 --> 00:30:37,480
Some people say that selling
put is like name your own price

475
00:30:37,480 --> 00:30:42,320
and get paid for trying it.

476
00:30:42,320 --> 00:30:55,430
And that's why we have this
famous trade, Warren Buffett,

477
00:30:55,430 --> 00:31:00,130
Berkshire, sold long dated puts
on four leading stock indices,

478
00:31:00,130 --> 00:31:03,910
in US, UK, Europe,
and Japan, collected

479
00:31:03,910 --> 00:31:09,610
about four billion premium
without posting collateral.

480
00:31:09,610 --> 00:31:14,980
Without posting collateral,
that was very important.

481
00:31:14,980 --> 00:31:18,010
This is something I
actually was very involved

482
00:31:18,010 --> 00:31:20,190
in one of my previous jobs.

483
00:31:20,190 --> 00:31:25,860
This happened about, I
think, around 2005, 2006.

484
00:31:25,860 --> 00:31:30,040
It's one of the biggest trades.

485
00:31:30,040 --> 00:31:35,450
And I was told when I
was involved with this,

486
00:31:35,450 --> 00:31:43,160
this was one of the biggest
cash outflow in the derivatives

487
00:31:43,160 --> 00:31:48,360
trades at that time,
because Warren Buffett

488
00:31:48,360 --> 00:31:50,510
collected the premium
without posting collateral.

489
00:31:53,320 --> 00:31:56,590
If he had agreed
to post collateral

490
00:31:56,590 --> 00:31:59,390
during the crisis
of 2008, he's going

491
00:31:59,390 --> 00:32:04,220
to post many billions of
dollars of collateral.

492
00:32:04,220 --> 00:32:07,890
And one reason he had more
cash than other people was

493
00:32:07,890 --> 00:32:12,248
he's very careful
[INAUDIBLE] and I

494
00:32:12,248 --> 00:32:14,550
think I put a reference
if you are interested

495
00:32:14,550 --> 00:32:18,522
and then you can essentially
see the [INAUDIBLE] link

496
00:32:18,522 --> 00:32:19,022
[INAUDIBLE].

497
00:32:26,390 --> 00:32:28,440
And what's interesting
is that, there

498
00:32:28,440 --> 00:32:33,580
were quite a few dealers who
are interested in this trade,

499
00:32:33,580 --> 00:32:37,090
but they know the size.

500
00:32:37,090 --> 00:32:39,795
And in a long-dated
equity option,

501
00:32:39,795 --> 00:32:43,090
it is not easy to handle,
but I think a lot of people

502
00:32:43,090 --> 00:32:46,040
were able to handle.

503
00:32:46,040 --> 00:32:54,090
To me, some people were not able
to trade or enter this trade,

504
00:32:54,090 --> 00:32:56,610
not because they could not
handle the equity risk.

505
00:32:56,610 --> 00:33:02,360
It's they could not
handle the CVA compounded.

506
00:33:02,360 --> 00:33:06,200
First of all, we
know there's a CVA.

507
00:33:06,200 --> 00:33:10,930
Essentially, we bought this
option from Warren Buffett.

508
00:33:10,930 --> 00:33:13,550
Eventually, he may need
to pay and at that time,

509
00:33:13,550 --> 00:33:17,210
he may default. So that's
a regular CVA risk.

510
00:33:17,210 --> 00:33:19,920
But this is also
a wrong-way risk,

511
00:33:19,920 --> 00:33:22,820
meaning a more severe risk.

512
00:33:22,820 --> 00:33:32,330
You can imagine when
the market sells off,

513
00:33:32,330 --> 00:33:38,100
Warren Buffet would
actually owe us more money.

514
00:33:38,100 --> 00:33:42,910
Do you think in that scenario he
will be more likely to default

515
00:33:42,910 --> 00:33:46,730
or less likely to default?

516
00:33:46,730 --> 00:33:49,260
He'll be more likely
to default. That's

517
00:33:49,260 --> 00:33:51,910
where the term
wrong-way risk comes in.

518
00:33:51,910 --> 00:33:55,320
When your counterparty owes
you more and more money,

519
00:33:55,320 --> 00:33:59,500
that's when he's more
likely to default.

520
00:33:59,500 --> 00:34:03,290
And that's even harder to model.

521
00:34:03,290 --> 00:34:06,220
And there's a
liquidity funding risk

522
00:34:06,220 --> 00:34:09,850
which can also be wrong-way,
because as a dealer

523
00:34:09,850 --> 00:34:14,510
you may need to come up
with a billion or two cash

524
00:34:14,510 --> 00:34:16,860
to pay Berkshire.

525
00:34:16,860 --> 00:34:19,219
Where do you get the money from?

526
00:34:19,219 --> 00:34:22,040
Typically, people
need to issue a debt

527
00:34:22,040 --> 00:34:25,760
to fund in a [? sine ?] secure
way and essentially, you'll

528
00:34:25,760 --> 00:34:30,870
pay for quite a
spread on your debt.

529
00:34:30,870 --> 00:34:37,969
That is essentially the cost
of your liquidity of funding.

530
00:34:37,969 --> 00:34:41,389
So what we did was,
essentially, we

531
00:34:41,389 --> 00:34:46,290
charged Warren Buffett
CVA and wrong-way CVA,

532
00:34:46,290 --> 00:34:50,840
charge of the funding costs,
some wrong-way funding costs.

533
00:34:50,840 --> 00:34:54,719
Another challenge, of course,
is that some dealers, I suspect,

534
00:34:54,719 --> 00:34:57,370
they could've priced
CVA, but they do not

535
00:34:57,370 --> 00:35:02,900
have a good CV trading
desk risk management

536
00:35:02,900 --> 00:35:07,740
to deliver risk management
of CVA and funding.

537
00:35:07,740 --> 00:35:11,750
Once you have this
position at hand,

538
00:35:11,750 --> 00:35:13,666
you have counterparty risks.

539
00:35:13,666 --> 00:35:17,640
But how do you hedge it?

540
00:35:17,640 --> 00:35:23,400
You charge Warren Buffet x
million dollars for the CVA.

541
00:35:23,400 --> 00:35:29,200
If you don't do anything,
when their spread widens,

542
00:35:29,200 --> 00:35:32,780
you're going to have
a lot more CVA loss.

543
00:35:32,780 --> 00:35:34,250
So you need to risk manage that.

544
00:35:37,810 --> 00:35:40,600
Of course, you can do
that with any hedge.

545
00:35:40,600 --> 00:35:47,870
But at any hedge, if we
drill down to details,

546
00:35:47,870 --> 00:35:50,150
you suffer a fair
amount of gap risk.

547
00:35:50,150 --> 00:35:52,050
It's not like a bond.

548
00:35:52,050 --> 00:35:56,210
If you own a bond, you
can buy a CDS protection

549
00:35:56,210 --> 00:35:57,160
on the same bond.

550
00:35:57,160 --> 00:36:01,840
More or less, you are hedged
for a while in a static way.

551
00:36:01,840 --> 00:36:03,860
But for a CVA, it's not.

552
00:36:03,860 --> 00:36:08,940
The reason for that is the
exposure can change over time.

553
00:36:08,940 --> 00:36:11,700
One thing we tried at
the time, essentially

554
00:36:11,700 --> 00:36:17,395
we sort of structured
like a credit-linked note

555
00:36:17,395 --> 00:36:19,510
type of trade.

556
00:36:19,510 --> 00:36:22,580
Essentially, you go to
people who own or would

557
00:36:22,580 --> 00:36:25,080
like to buy Berkshire's bond.

558
00:36:25,080 --> 00:36:27,140
Essentially, you
should tell them OK,

559
00:36:27,140 --> 00:36:31,590
we have a credit asset
similar to Berkshire's bond.

560
00:36:31,590 --> 00:36:34,940
If you feel comfortable with
owning Berkshire's bond,

561
00:36:34,940 --> 00:36:42,030
you may consider our asset
which pays more coupon.

562
00:36:42,030 --> 00:36:44,000
And the reason we were
able to pay more coupon

563
00:36:44,000 --> 00:36:47,600
is we were able to charge
Berkshire a lot of money.

564
00:36:50,690 --> 00:36:53,750
And there's also a tranched
portfolio protection

565
00:36:53,750 --> 00:36:55,300
thing that's involved,
but I'm going

566
00:36:55,300 --> 00:36:59,910
to skip that for
the sake of time.

567
00:36:59,910 --> 00:37:03,220
So then the question is the
we charged a lot of the money

568
00:37:03,220 --> 00:37:04,950
from Berkshire.

569
00:37:04,950 --> 00:37:07,430
Why would he want
to do this trade?

570
00:37:07,430 --> 00:37:09,270
What would they think?

571
00:37:09,270 --> 00:37:11,240
So here's my guess.

572
00:37:11,240 --> 00:37:14,670
As you know, they have
an insurance business.

573
00:37:14,670 --> 00:37:18,970
Then they wanted to explore
other ways to sell insurance.

574
00:37:18,970 --> 00:37:22,050
So selling puts essentially
is spreading insurance

575
00:37:22,050 --> 00:37:23,375
on the equity market.

576
00:37:26,900 --> 00:37:34,550
They sold like 10,
15 year maturity

577
00:37:34,550 --> 00:37:38,530
puts at below their spots.

578
00:37:38,530 --> 00:37:40,460
So then people can
think, OK, what's

579
00:37:40,460 --> 00:37:47,260
the likelihood of a
stock price coming down

580
00:37:47,260 --> 00:37:50,275
to below the current
stock in 10, 15 years.

581
00:37:50,275 --> 00:37:53,720
Well, it happens, but
it's not very likely.

582
00:37:53,720 --> 00:37:57,480
And they do have a
day one cash inflow.

583
00:37:57,480 --> 00:38:01,150
So essentially, I think one
way Berkshire was thinking

584
00:38:01,150 --> 00:38:04,351
is that they thought
low funding costs.

585
00:38:04,351 --> 00:38:06,620
If you read Warren
Buffett's paper,

586
00:38:06,620 --> 00:38:09,580
essentially he's saying
it's like 1% interest rate

587
00:38:09,580 --> 00:38:15,400
on a 10 year cash, or
something like that.

588
00:38:15,400 --> 00:38:19,880
And it's very important to
manage your liquidity well.

589
00:38:19,880 --> 00:38:25,400
They do not have any cash
flow until the trade matures.

590
00:38:25,400 --> 00:38:31,680
So that's how they avoided the
cash flow drain during 2008,

591
00:38:31,680 --> 00:38:35,440
even though they did suffer
unrealized mark-to-market loss.

592
00:38:39,090 --> 00:38:42,550
But what's interesting is
that during 2008, 2009,

593
00:38:42,550 --> 00:38:44,740
Berkshire did explore
the feasibility

594
00:38:44,740 --> 00:38:48,230
of posting collateral.

595
00:38:48,230 --> 00:38:52,794
This started with no
collateral posting.

596
00:38:52,794 --> 00:38:54,460
But then they wanted
to post collateral.

597
00:38:54,460 --> 00:38:57,130
They actually approached some
of the dealers saying oh, I

598
00:38:57,130 --> 00:39:00,150
want to post some collateral.

599
00:39:00,150 --> 00:39:02,990
Why is that?

600
00:39:02,990 --> 00:39:05,190
There's no free lunch.

601
00:39:05,190 --> 00:39:09,990
So what happened was they were
smart not to post collateral,

602
00:39:09,990 --> 00:39:13,340
but during the crisis
their spread widened.

603
00:39:13,340 --> 00:39:15,350
Everyone's spread widened.

604
00:39:15,350 --> 00:39:17,840
So Berkshire's spread widened.

605
00:39:17,840 --> 00:39:21,070
Then Warren Buffett
owed more money.

606
00:39:21,070 --> 00:39:22,270
So guess what?

607
00:39:22,270 --> 00:39:25,940
The CVA hedging would
require the dealer

608
00:39:25,940 --> 00:39:30,029
to buy more and more
protection on Berkshire.

609
00:39:30,029 --> 00:39:31,570
When you buy more
and more protection

610
00:39:31,570 --> 00:39:37,110
on someone, that will
actually drive that person's,

611
00:39:37,110 --> 00:39:39,270
that entity's, credit
spread even wider.

612
00:39:42,500 --> 00:39:46,860
So Berkshire essentially saw
their credit spread widening

613
00:39:46,860 --> 00:39:52,370
a lot more than they had hoped
for, than they had anticipated.

614
00:39:52,370 --> 00:39:55,900
And later on, they found out
it was due to CVA hedging,

615
00:39:55,900 --> 00:39:59,350
CVA risk management.

616
00:39:59,350 --> 00:40:02,500
That actually affected
their bond issuance.

617
00:40:02,500 --> 00:40:07,110
When you have a high credit
spread from CDS market,

618
00:40:07,110 --> 00:40:09,910
essentially the cash
market may actually

619
00:40:09,910 --> 00:40:12,300
question may actually follow.

620
00:40:12,300 --> 00:40:15,560
And whoever would like
to buy Berkshire's bond

621
00:40:15,560 --> 00:40:16,900
would think twice.

622
00:40:16,900 --> 00:40:19,600
OK, if I have to buy
this bond, if I ever

623
00:40:19,600 --> 00:40:21,940
have to buy credit
protection, it's

624
00:40:21,940 --> 00:40:25,270
going to cost me a lot more
money because of the spread

625
00:40:25,270 --> 00:40:25,970
widening.

626
00:40:25,970 --> 00:40:29,520
So therefore, I'm going
to demand higher coupon

627
00:40:29,520 --> 00:40:33,752
on Berkshire's bond, and that
drives their funding cost high.

628
00:40:33,752 --> 00:40:36,242
So they explored in
different to post collateral.

629
00:40:38,750 --> 00:40:42,396
Another thing of course is a
very interesting thing to ask.

630
00:40:42,396 --> 00:40:44,580
Berkshire thinks
they're making money

631
00:40:44,580 --> 00:40:46,090
and the dealer
thinks they're making

632
00:40:46,090 --> 00:40:49,630
money, which is probably true.

633
00:40:49,630 --> 00:40:55,580
But then the question
is, who is losing money

634
00:40:55,580 --> 00:40:56,980
or who will lose money.

635
00:41:00,170 --> 00:41:01,230
Anyone has any ideas?

636
00:41:12,630 --> 00:41:15,590
I think there's probably
a lot of answers to this.

637
00:41:15,590 --> 00:41:18,880
My view is that essentially
whoever needs to hedge,

638
00:41:18,880 --> 00:41:23,190
whoever need to buy put.

639
00:41:23,190 --> 00:41:31,080
If the market doesn't decline as
much as much as you hoped for,

640
00:41:31,080 --> 00:41:33,180
essentially you'll
pay for put premium

641
00:41:33,180 --> 00:41:34,765
and do not get the benefits.

642
00:41:41,060 --> 00:41:43,180
Here's an interesting
CV conundrum.

643
00:41:43,180 --> 00:41:46,870
Now, hopefully by
this time, you guys

644
00:41:46,870 --> 00:41:51,345
fully appreciate the CVA
risks and the impact of CVA.

645
00:41:56,320 --> 00:41:59,880
In terms of risk itself,
in terms of magnitude,

646
00:41:59,880 --> 00:42:02,330
as I mentioned earlier
being the crisis,

647
00:42:02,330 --> 00:42:05,670
2008 crisis, which
[? killed ?] among easily

648
00:42:05,670 --> 00:42:10,420
billions of dollars loss for
some of the firms due to CVA,

649
00:42:10,420 --> 00:42:15,910
and that's more than
the actual default loss.

650
00:42:15,910 --> 00:42:18,950
Now given you know
the CVA, so if you

651
00:42:18,950 --> 00:42:22,130
trade with counterparty
A, naturally you'll say

652
00:42:22,130 --> 00:42:25,370
you want to think OK,
I want buy protection

653
00:42:25,370 --> 00:42:31,330
to hedge my CVA risk, to
buy credit protection on A,

654
00:42:31,330 --> 00:42:37,830
from counterparty B. If you
trade with counterparty B,

655
00:42:37,830 --> 00:42:43,920
you would have CVA
against counterparty B.

656
00:42:43,920 --> 00:42:47,015
You would have a credit
risk against counterparty B.

657
00:42:47,015 --> 00:42:49,280
So what are you going to do?

658
00:42:49,280 --> 00:42:57,160
If you just follow
the simple thinking,

659
00:42:57,160 --> 00:42:58,980
essentially you may
think oh OK, maybe I

660
00:42:58,980 --> 00:43:07,480
should buy credit protection
on B from counterparty C.

661
00:43:07,480 --> 00:43:12,740
But if you were to do that, then
you have to continue on that.

662
00:43:12,740 --> 00:43:15,260
It becomes an infinite series.

663
00:43:18,010 --> 00:43:21,730
Infinite series are OK
I'll say theoretically,

664
00:43:21,730 --> 00:43:24,676
but in practice I
feel it's going to be

665
00:43:24,676 --> 00:43:25,800
very challenging to handle.

666
00:43:29,570 --> 00:43:32,470
So what would be
a simple strategy

667
00:43:32,470 --> 00:43:37,850
to actually terminate this
infinite series quickly?

668
00:43:52,320 --> 00:43:57,640
Yeah this also has theoretical
implications for CVA pricing.

669
00:43:57,640 --> 00:44:02,270
Sometimes we say, OK, arbitrage
pricing is really replication,

670
00:44:02,270 --> 00:44:03,430
use hedge instruments.

671
00:44:03,430 --> 00:44:06,840
Now, you have to use an infinite
number of hedge instruments.

672
00:44:06,840 --> 00:44:11,040
That's going to impact your
[? replication ?] modeling.

673
00:44:13,820 --> 00:44:16,860
So the way we would
do it practically

674
00:44:16,860 --> 00:44:21,380
is to buy credit protection
on A from counterparty B fully

675
00:44:21,380 --> 00:44:25,180
collateralized,
typically from a dealer.

676
00:44:25,180 --> 00:44:30,370
So however much money you owe
from counterparty B right away,

677
00:44:30,370 --> 00:44:32,110
they're going to
post collateral.

678
00:44:32,110 --> 00:44:36,120
In a way, it's more or less
similar to a futures context

679
00:44:36,120 --> 00:44:37,510
settling.

680
00:44:37,510 --> 00:44:41,730
That minimized the
counterparty risk [INAUDIBLE].

681
00:44:41,730 --> 00:44:45,950
So you can cut off this
infinite series easily.

682
00:44:53,730 --> 00:44:56,770
Here, I'd like to
touch upon what

683
00:44:56,770 --> 00:44:59,740
I call enterprise-level
derivatives modeling.

684
00:45:03,010 --> 00:45:05,770
We mentioned trade-level
derivatives models.

685
00:45:05,770 --> 00:45:09,940
That is essentially, is
just a regular model.

686
00:45:09,940 --> 00:45:11,890
When people talk about
derivatives model,

687
00:45:11,890 --> 00:45:14,940
usually people talk
about trade-level models.

688
00:45:14,940 --> 00:45:18,830
Essentially, you model
each trade independently.

689
00:45:18,830 --> 00:45:21,700
Your model is price,
mark-to-market

690
00:45:21,700 --> 00:45:25,000
or its Greeks sensitivity.

691
00:45:25,000 --> 00:45:27,200
Then when you have a
portfolio of these trades,

692
00:45:27,200 --> 00:45:29,530
essentially you
can just aggregate

693
00:45:29,530 --> 00:45:35,640
their PV, their Greeks,
through linear aggregation.

694
00:45:35,640 --> 00:45:37,880
Then essentially you get
the PV of the portfolio.

695
00:45:43,130 --> 00:45:47,160
But as we have
seen already, that

696
00:45:47,160 --> 00:45:50,280
doesn't capture the
complete picture.

697
00:45:50,280 --> 00:45:57,290
There are additional risks
that require further modeling.

698
00:45:57,290 --> 00:45:59,870
One is non-linear
portfolio risks.

699
00:46:02,880 --> 00:46:08,090
So essentially, these risks
cannot be like a linear

700
00:46:08,090 --> 00:46:13,890
aggregation of the risks of
each of the component trades

701
00:46:13,890 --> 00:46:15,340
in the portfolio.

702
00:46:15,340 --> 00:46:18,170
The example we have
gone through is CVA,

703
00:46:18,170 --> 00:46:22,170
funding is of similar
nature, capital liquidity

704
00:46:22,170 --> 00:46:25,920
are also examples.

705
00:46:25,920 --> 00:46:30,680
The key to handle
this situation is

706
00:46:30,680 --> 00:46:34,200
to be able to model
all the trades

707
00:46:34,200 --> 00:46:37,600
in the market and the market
risk factors of a portfolio

708
00:46:37,600 --> 00:46:40,890
consistently so that you
can handle the offsetting

709
00:46:40,890 --> 00:46:42,520
trades properly.

710
00:46:45,330 --> 00:46:50,180
Of course, we need to
leverage the trade-level model

711
00:46:50,180 --> 00:46:54,330
essentially to price each
individual trade as of today,

712
00:46:54,330 --> 00:46:55,622
as of a future date.

713
00:46:58,230 --> 00:47:02,177
What's interesting is
that there's also feedback

714
00:47:02,177 --> 00:47:03,260
to the trade-level models.

715
00:47:06,120 --> 00:47:09,030
For instance, when we
price a cancellable

716
00:47:09,030 --> 00:47:12,180
swap of a very public trade.

717
00:47:12,180 --> 00:47:16,420
Now this cancellable swap we
trade with a counterparty,

718
00:47:16,420 --> 00:47:18,360
let's say assumed
uncollateralized,

719
00:47:18,360 --> 00:47:25,900
we trade with a counterparty
that's close to default.

720
00:47:25,900 --> 00:47:27,730
You know the trade-level
model doesn't

721
00:47:27,730 --> 00:47:31,410
know about this
counterparty, about default.

722
00:47:31,410 --> 00:47:36,650
The trade-level will give
you independent, the exercise

723
00:47:36,650 --> 00:47:41,350
boundaries, when do you need
to cancel the swap, independent

724
00:47:41,350 --> 00:47:44,970
of the counterparty
credit quality.

725
00:47:44,970 --> 00:47:49,310
That invites a question,
when the counterparty is

726
00:47:49,310 --> 00:47:53,930
close to default, even if your
model says OK, you should not

727
00:47:53,930 --> 00:47:59,092
exercise based on the
market conditions,

728
00:47:59,092 --> 00:48:02,710
but shouldn't we consider the
counterparty condition, credit

729
00:48:02,710 --> 00:48:05,200
condition.

730
00:48:05,200 --> 00:48:07,860
If the counterparty
were close to default,

731
00:48:07,860 --> 00:48:11,220
if you cancel the swap
sooner essentially you'll

732
00:48:11,220 --> 00:48:17,420
eliminate or reduce
the counterparty risk.

733
00:48:17,420 --> 00:48:22,820
This is actually interesting
application and feedback

734
00:48:22,820 --> 00:48:28,430
between a trade-level model and
the enterprise-level models.

735
00:48:28,430 --> 00:48:31,920
So what we did was, in
some of my previous jobs,

736
00:48:31,920 --> 00:48:37,870
what we did was actually figure
out the counterparty risk

737
00:48:37,870 --> 00:48:40,550
in these trades,
the major trades.

738
00:48:40,550 --> 00:48:43,920
Then essentially, we just
tell the underlying trader,

739
00:48:43,920 --> 00:48:47,190
if you were to
cancel this trade,

740
00:48:47,190 --> 00:48:51,090
we have a benefit because
we're going to reduce

741
00:48:51,090 --> 00:48:54,930
the CVA or even zero out CVA.

742
00:48:54,930 --> 00:48:57,950
So the CV trader would be able
to pay the underlying trader.

743
00:48:57,950 --> 00:49:01,080
So therefore, the
underlying model actually

744
00:49:01,080 --> 00:49:04,890
can take this as
input rather than

745
00:49:04,890 --> 00:49:11,280
as part of the exercise
condition modeling,

746
00:49:11,280 --> 00:49:14,680
knowing if you cancel
earlier you potentially

747
00:49:14,680 --> 00:49:16,746
can get additional benefits.

748
00:49:16,746 --> 00:49:19,596
This model may eventually
be able to tell

749
00:49:19,596 --> 00:49:26,180
you to handle the risks more
properly, market risks together

750
00:49:26,180 --> 00:49:29,070
with counterparty risks.

751
00:49:29,070 --> 00:49:34,870
This is roughly the
scope and the application

752
00:49:34,870 --> 00:49:36,730
of the enterprise-level model.

753
00:49:41,280 --> 00:49:46,230
This is actually a fairly
significant modelling effort

754
00:49:46,230 --> 00:49:51,620
as well as significant
infrastructure and data effort.

755
00:49:51,620 --> 00:49:53,782
Essentially, it
requires a fair amount

756
00:49:53,782 --> 00:49:57,180
of martingale testing,
martingale resampling,

757
00:49:57,180 --> 00:50:00,930
martingale interpolation
and the martingale modeling.

758
00:50:00,930 --> 00:50:07,180
The reason for that is
you have a trade model,

759
00:50:07,180 --> 00:50:14,450
and each trade model can model
a particular trade accurately,

760
00:50:14,450 --> 00:50:20,290
and there's certain market
modeling, simulations

761
00:50:20,290 --> 00:50:25,470
of the underlying
market or great PDE.

762
00:50:25,470 --> 00:50:30,750
But when you put a portfolio
of trades together,

763
00:50:30,750 --> 00:50:35,290
now the methodology you use for
modeling one trade accurately

764
00:50:35,290 --> 00:50:40,540
may not necessarily be the
methodology you need to model

765
00:50:40,540 --> 00:50:43,422
all the trades accurately.

766
00:50:43,422 --> 00:50:46,310
Some of these require PDE
and some require simulations,

767
00:50:46,310 --> 00:50:48,160
but you need to
put them together.

768
00:50:48,160 --> 00:50:49,610
Typically, we use simulation.

769
00:50:49,610 --> 00:50:53,700
And that introduced
numerical inaccuracies.

770
00:50:53,700 --> 00:50:55,255
And the martingale
testing will tell

771
00:50:55,255 --> 00:50:58,240
us are we introducing
a lot of errors,

772
00:50:58,240 --> 00:51:00,180
martingale resampling
essentially

773
00:51:00,180 --> 00:51:03,100
would allow us to
correct the errors.

774
00:51:03,100 --> 00:51:07,960
As you know, the
martingale is a foundation

775
00:51:07,960 --> 00:51:10,760
of the arbitrage pricing.

776
00:51:10,760 --> 00:51:13,030
Essentially,
martingale resampling

777
00:51:13,030 --> 00:51:18,110
will actually be able to enforce
the martingale conditions

778
00:51:18,110 --> 00:51:22,900
in the numerical procedure,
not only theoretically.

779
00:51:22,900 --> 00:51:24,630
Martingale
interpolation modeling

780
00:51:24,630 --> 00:51:29,835
are other important interesting
aspects if we have time we can

781
00:51:29,835 --> 00:51:39,960
[INAUDIBLE] There are
different approaches

782
00:51:39,960 --> 00:51:42,340
for how to do it
in a systematic way

783
00:51:42,340 --> 00:51:47,620
and still remain
additional ways.

784
00:51:47,620 --> 00:51:51,770
I'd like to quickly go
over some of the examples

785
00:51:51,770 --> 00:51:54,870
of martingale and
martingale measures.

786
00:51:54,870 --> 00:52:00,920
I may need to go through this
quite quickly due to the time

787
00:52:00,920 --> 00:52:01,950
limitations.

788
00:52:01,950 --> 00:52:06,350
But hopefully, you guys have
learned all these already.

789
00:52:06,350 --> 00:52:09,680
This will hopefully be more
like a review for you guys.

790
00:52:09,680 --> 00:52:12,620
So essentially, we are
talking about a few examples.

791
00:52:12,620 --> 00:52:14,950
What's the martingale
measure for forward price,

792
00:52:14,950 --> 00:52:18,810
forward LIBOR, forward
price, forward FX rate,

793
00:52:18,810 --> 00:52:20,660
forward CDS par coupon.

794
00:52:20,660 --> 00:52:26,710
I would hope you guys would
know the first few already.

795
00:52:26,710 --> 00:52:28,600
The for CDS par
coupon in my view

796
00:52:28,600 --> 00:52:31,650
is actually fairly challenging.

797
00:52:31,650 --> 00:52:35,540
For simplicity, I'm not
considering the collateral

798
00:52:35,540 --> 00:52:38,470
discounting explicitly.

799
00:52:38,470 --> 00:52:46,190
That adds additional challenges
but still we can address that.

800
00:52:46,190 --> 00:52:52,890
So under the risk
neutral measure,

801
00:52:52,890 --> 00:53:00,810
essentially for
this Y of t being

802
00:53:00,810 --> 00:53:05,480
the price of a traded asset
with no intermediate cash flow.

803
00:53:05,480 --> 00:53:13,740
Essentially, that is y_T
over beta(t) is a martingale.

804
00:53:13,740 --> 00:53:16,380
This is essentially the
Harrison-Pliska martingale

805
00:53:16,380 --> 00:53:18,560
no-arbitrage theorem.

806
00:53:18,560 --> 00:53:23,000
It says for two traded assets
with no intermediate cash

807
00:53:23,000 --> 00:53:27,590
flows, satisfying
technical conditions,

808
00:53:27,590 --> 00:53:29,900
the ratio is a martingale.

809
00:53:29,900 --> 00:53:33,740
There's a probability
measure corresponding

810
00:53:33,740 --> 00:53:36,580
to the numeraire asset.

811
00:53:36,580 --> 00:53:42,400
Therefore, naturally
we have this composite.

812
00:53:42,400 --> 00:53:44,770
The forward
arbitrage-free measure

813
00:53:44,770 --> 00:53:48,890
essentially corresponding to a
numeraire of zero-coupon bonds.

814
00:53:48,890 --> 00:53:54,595
Naturally, we can
find this Y_t and P(t,

815
00:53:54,595 --> 00:53:58,050
T) ratio is a martingale.

816
00:53:58,050 --> 00:54:01,650
Again, it's just a ratio
of two traded assets

817
00:54:01,650 --> 00:54:06,440
with no intermediate cash flow.

818
00:54:06,440 --> 00:54:09,930
From the definition
of the forward price,

819
00:54:09,930 --> 00:54:13,580
essentially the forward
price is a martingale

820
00:54:13,580 --> 00:54:15,300
under the forward measure.

821
00:54:18,460 --> 00:54:22,340
Forward LIBOR-- this is the
forward LIBOR-- essentially,

822
00:54:22,340 --> 00:54:24,720
it's a ratio of two
zero-coupon bonds.

823
00:54:24,720 --> 00:54:27,440
So naturally, we know
it's a martingale under

824
00:54:27,440 --> 00:54:30,020
of the numeraire asset.

825
00:54:30,020 --> 00:54:33,830
So essentially it's a forward
measure up to the payment

826
00:54:33,830 --> 00:54:36,370
on the forward LIBOR.

827
00:54:36,370 --> 00:54:39,750
So this is the
martingale condition.

828
00:54:39,750 --> 00:54:42,920
Similarly, we can do this
argument of the forward swap

829
00:54:42,920 --> 00:54:43,420
rate.

830
00:54:46,250 --> 00:54:53,540
Essentially, a
forward swap rate is,

831
00:54:53,540 --> 00:55:00,430
we can start with, like
an annuity numeraire.

832
00:55:00,430 --> 00:55:03,240
And since the forward swap
rate, you essentially know,

833
00:55:03,240 --> 00:55:07,210
is the difference of
two zero-coupon bonds

834
00:55:07,210 --> 00:55:08,780
divided by annuity.

835
00:55:08,780 --> 00:55:12,580
And therefore we
can conclude based

836
00:55:12,580 --> 00:55:17,280
on Harrison-Pliska theorem the
forward swap rate essentially

837
00:55:17,280 --> 00:55:21,380
is the martingale under
the annuity measure,

838
00:55:21,380 --> 00:55:24,390
with this annuity
as the numeraire.

839
00:55:28,140 --> 00:55:33,520
The same argument goes
for the forward FX rate.

840
00:55:33,520 --> 00:55:36,280
Mainly the idea is or the
pattern you probably have seen

841
00:55:36,280 --> 00:55:42,230
is, for any quantity you see
if you can find two assets

842
00:55:42,230 --> 00:55:47,560
and then use these two
asset ratio to represent

843
00:55:47,560 --> 00:55:49,200
this in a quantity.

844
00:55:49,200 --> 00:55:56,980
So the forward FX essentially
is a ratio like this.

845
00:55:56,980 --> 00:56:01,560
This is nothing more than
the interest rate parity.

846
00:56:01,560 --> 00:56:10,760
From the spot you
grow both [INAUDIBLE].

847
00:56:10,760 --> 00:56:14,190
You start with spot, you
grow the domestic currency

848
00:56:14,190 --> 00:56:16,590
and then you grow
the foreign currency.

849
00:56:16,590 --> 00:56:18,430
You get FX forwards.

850
00:56:18,430 --> 00:56:22,260
And FX forward is a
martingale measure

851
00:56:22,260 --> 00:56:24,530
under the domestic
forward measure.

852
00:56:29,670 --> 00:56:40,120
This is a simple technique to do
change of probability measure.

853
00:56:40,120 --> 00:56:46,380
It's roughly how I remember
change of probability measure

854
00:56:46,380 --> 00:56:49,710
and Radon-Nikodym derivatives.

855
00:56:49,710 --> 00:56:54,120
You essentially start
with, again, martingale,

856
00:56:54,120 --> 00:57:04,900
assuming this is martingale
under a particular measure

857
00:57:04,900 --> 00:57:07,820
corresponding to
the numeraire asset.

858
00:57:07,820 --> 00:57:11,090
And then this quantity
is also a martingale

859
00:57:11,090 --> 00:57:13,490
under a different
measure corresponding

860
00:57:13,490 --> 00:57:19,110
to a different numeraire asset.

861
00:57:19,110 --> 00:57:24,530
One key point is when you change
probability measure essentially

862
00:57:24,530 --> 00:57:26,960
you change the
numeraire corresponding

863
00:57:26,960 --> 00:57:29,430
to the probability measure.

864
00:57:29,430 --> 00:57:32,330
And therefore essentially
the important thing

865
00:57:32,330 --> 00:57:42,910
is we know the PV or the
mark-to-market, of a traded

866
00:57:42,910 --> 00:57:44,640
security is measure-independent.

867
00:57:47,320 --> 00:57:49,350
It doesn't matter
what mathematics

868
00:57:49,350 --> 00:57:53,710
you use if the traded
security is going

869
00:57:53,710 --> 00:57:55,950
to match the market price.

870
00:57:55,950 --> 00:58:01,080
And therefore, you can
price this security

871
00:58:01,080 --> 00:58:05,470
under one measure
or one numeraire.

872
00:58:05,470 --> 00:58:09,130
And then you can price
again with another measure,

873
00:58:09,130 --> 00:58:11,750
another numeraire.

874
00:58:11,750 --> 00:58:13,890
They've got to be the same.

875
00:58:13,890 --> 00:58:17,080
Then naturally, you see
this simple equation

876
00:58:17,080 --> 00:58:20,250
as the starting point to
do the change of measure.

877
00:58:20,250 --> 00:58:25,530
If you just simply change the
variables, then essentially

878
00:58:25,530 --> 00:58:29,810
you get your change
of measure as well as

879
00:58:29,810 --> 00:58:31,730
Radon-Nikodym derivative.

880
00:58:31,730 --> 00:58:34,140
And if you worked
on the BGM model,

881
00:58:34,140 --> 00:58:38,370
you'll probably recognize
this change of measure

882
00:58:38,370 --> 00:58:42,860
which is used for the BGM
model under the old measure.

883
00:58:45,930 --> 00:58:50,470
Now here's the subtlety,
credit derivatives.

884
00:58:50,470 --> 00:58:55,310
Naturally, people would think
OK, since the forward swap

885
00:58:55,310 --> 00:58:59,570
rate is a martingale
under the annuity

886
00:58:59,570 --> 00:59:06,390
measure, naturally people would
think OK, then forward CDS par

887
00:59:06,390 --> 00:59:09,762
rate, it's like a
forward swap rate.

888
00:59:09,762 --> 00:59:18,200
It's got to be a martingale
under the risky annuity

889
00:59:18,200 --> 00:59:20,470
measure.

890
00:59:20,470 --> 00:59:25,820
So that's quite intuitive
except there's one problem.

891
00:59:25,820 --> 00:59:31,630
If the reference
credit entity has

892
00:59:31,630 --> 00:59:35,860
zero recovery upon
default. Then,

893
00:59:35,860 --> 00:59:40,090
this risky annuity
could have a 0.

894
00:59:40,090 --> 00:59:42,470
And now we're
talking about we want

895
00:59:42,470 --> 00:59:48,370
to use something that could
be 0 as our numeraire.

896
00:59:48,370 --> 00:59:54,510
How do we resolve the
technical mathematical problem.

897
00:59:54,510 --> 00:59:56,314
So that actually
very interesting.

898
01:00:02,000 --> 01:00:04,990
Schönbucher was the first person
who published a paper on this

899
01:00:04,990 --> 01:00:07,590
model.

900
01:00:07,590 --> 01:00:10,120
I was just trying to
do some work myself

901
01:00:10,120 --> 01:00:12,230
when I was working on BGM model.

902
01:00:12,230 --> 01:00:17,770
I thought oh, it would've been
nice to expand the BGM model

903
01:00:17,770 --> 01:00:21,470
to the credit derivatives.

904
01:00:21,470 --> 01:00:25,740
But then immediately I
stumbled with this difficulty

905
01:00:25,740 --> 01:00:28,600
where when the
recovery is 0, you're

906
01:00:28,600 --> 01:00:30,760
going to have a 0
in your numeraire,

907
01:00:30,760 --> 01:00:33,080
in your risky annuity.

908
01:00:36,740 --> 01:00:45,070
So Schönbucher, essentially,
his idea was let's focus

909
01:00:45,070 --> 01:00:51,980
on survival measures, meaning we
have a difficulty if a default

910
01:00:51,980 --> 01:00:56,520
happens and the recovery is 0.

911
01:00:56,520 --> 01:00:58,598
Now his idea is let's
forget about that state.

912
01:01:01,360 --> 01:01:02,490
Let's not worry about that.

913
01:01:09,750 --> 01:01:12,520
One immediate
question people will

914
01:01:12,520 --> 01:01:17,740
ask, if that's the
case, the probability

915
01:01:17,740 --> 01:01:21,280
measure, physical
probability measure

916
01:01:21,280 --> 01:01:23,820
or risk-neutral
probability measure,

917
01:01:23,820 --> 01:01:28,880
and this survival probability
measure are not equivalent

918
01:01:28,880 --> 01:01:33,050
because the survival probability
measure knows nothing

919
01:01:33,050 --> 01:01:35,710
about the default event.

920
01:01:35,710 --> 01:01:38,170
So they are not equivalent.

921
01:01:38,170 --> 01:01:43,070
That's, essentially,
you actually

922
01:01:43,070 --> 01:01:47,160
transform one mathematical
difficulty to another one.

923
01:01:47,160 --> 01:01:49,190
Luckily, the second
one turns out

924
01:01:49,190 --> 01:01:52,370
to be actually easier to solve.

925
01:01:52,370 --> 01:01:58,270
So the starting point is again
using Harrison-Pliska theorem.

926
01:01:58,270 --> 01:02:01,220
Essentially, you
just need to identify

927
01:02:01,220 --> 01:02:07,980
like a numeraire asset,
and the denominator assets.

928
01:02:10,990 --> 01:02:12,650
You identify two assets.

929
01:02:12,650 --> 01:02:17,700
You make a ratio and then
those are a martingale.

930
01:02:17,700 --> 01:02:20,770
So essentially this is forward
swap rate and forward annuity.

931
01:02:27,080 --> 01:02:37,160
If we have this indicator of
the default time of j-th credit

932
01:02:37,160 --> 01:02:41,450
name, greater than this
t, essentially this

933
01:02:41,450 --> 01:02:45,025
is like the premium leg of CDS.

934
01:02:47,610 --> 01:02:50,190
That's a traded asset.

935
01:02:50,190 --> 01:02:52,120
So therefore, we have a
martingale [INAUDIBLE]

936
01:02:52,120 --> 01:02:54,500
like this.

937
01:02:54,500 --> 01:02:57,650
The subtlety as you
probably can envision

938
01:02:57,650 --> 01:03:00,541
is going to come in when we
do the change of probability

939
01:03:00,541 --> 01:03:01,040
measures.

940
01:03:08,050 --> 01:03:12,360
OK, so we have talked
about how are we

941
01:03:12,360 --> 01:03:20,780
going to find the martingale
measure of a CDS par coupon

942
01:03:20,780 --> 01:03:24,730
or forward CDS par rate.

943
01:03:24,730 --> 01:03:27,950
This is a starting point
of martingale model.

944
01:03:27,950 --> 01:03:29,510
Essentially, for
any quantity you

945
01:03:29,510 --> 01:03:36,170
want to model you try to
find its martingale measure.

946
01:03:36,170 --> 01:03:38,040
Once you find this
martingale measure,

947
01:03:38,040 --> 01:03:41,290
you can do a martingale
representation.

948
01:03:41,290 --> 01:03:45,080
And then often times you need
to a change of a probability

949
01:03:45,080 --> 01:03:46,040
measure.

950
01:03:46,040 --> 01:03:48,480
So that all the term
structure functions,

951
01:03:48,480 --> 01:03:51,790
a consequence of a
variables are modeled

952
01:03:51,790 --> 01:03:55,410
in a consistent
probability measure.

953
01:03:55,410 --> 01:03:58,550
So finding the martingale
measure is the first point.

954
01:04:02,230 --> 01:04:07,170
Survival probability
measure, essentially, he just

955
01:04:07,170 --> 01:04:09,130
defined this with.

956
01:04:09,130 --> 01:04:14,350
You can define this
Radon-Nikodym derivative.

957
01:04:14,350 --> 01:04:19,355
Once you define
that essentially--

958
01:04:19,355 --> 01:04:25,210
if you remember the
previous formula--

959
01:04:25,210 --> 01:04:29,421
you will have a martingale
condition like this.

960
01:04:29,421 --> 01:04:41,080
[INAUDIBLE] The
probability measures

961
01:04:41,080 --> 01:04:45,610
are not equivalent
anymore, but yet they

962
01:04:45,610 --> 01:04:52,320
can still do change of
probability measure.

963
01:04:52,320 --> 01:04:56,650
You need to
separately model what

964
01:04:56,650 --> 01:04:58,380
going to happen when
the default happens

965
01:04:58,380 --> 01:04:59,830
if you want to use this model.

966
01:05:03,400 --> 01:05:09,365
Now, I'd like to move onto
the second part, martingale,

967
01:05:09,365 --> 01:05:10,740
martingale testing
and martingale

968
01:05:10,740 --> 01:05:13,090
resampling and interpolation.

969
01:05:13,090 --> 01:05:15,465
Martingale testing essentially
given the previously model

970
01:05:15,465 --> 01:05:17,500
formula's conditions.

971
01:05:17,500 --> 01:05:19,340
Those are, by the
way, just examples.

972
01:05:19,340 --> 01:05:21,070
There are a lot more.

973
01:05:21,070 --> 01:05:23,020
Essentially, you
know that's what

974
01:05:23,020 --> 01:05:25,020
it should be
theoretically you just

975
01:05:25,020 --> 01:05:28,610
test in your numerical
implementation

976
01:05:28,610 --> 01:05:32,080
and see if those
conditions are satisfied.

977
01:05:32,080 --> 01:05:34,210
That's the martingale test.

978
01:05:34,210 --> 01:05:37,735
Martingale resampling is we
know most likely if you were

979
01:05:37,735 --> 01:05:40,460
to test, we're going to fail.

980
01:05:40,460 --> 01:05:44,030
This is not necessarily
for enterprise-level models

981
01:05:44,030 --> 01:05:47,300
but even for trade-level
derivatives models.

982
01:05:47,300 --> 01:05:50,780
A lot of times, I think the
martingale conditions are not

983
01:05:50,780 --> 01:05:52,900
exactly satisfied.

984
01:05:52,900 --> 01:05:59,100
So one way to do that, is
to correct that, correct

985
01:05:59,100 --> 01:06:00,810
this error.

986
01:06:00,810 --> 01:06:04,190
The rationale is
essentially because

987
01:06:04,190 --> 01:06:07,990
of a numerical approximations.

988
01:06:07,990 --> 01:06:10,960
Whatever quantity
we model essentially

989
01:06:10,960 --> 01:06:13,030
is not a true quantity.

990
01:06:13,030 --> 01:06:15,000
The true quantity
we model essentially

991
01:06:15,000 --> 01:06:21,410
is some function of what
we have in our model.

992
01:06:21,410 --> 01:06:23,710
So therefore, you expect
a certain function.

993
01:06:23,710 --> 01:06:26,180
Sometimes you can have a
linear, log-linear function.

994
01:06:30,450 --> 01:06:34,890
This X_0 is what we
have in our model,

995
01:06:34,890 --> 01:06:40,690
and then X is what
we need to satisfy

996
01:06:40,690 --> 01:06:43,060
the martingale condition.

997
01:06:43,060 --> 01:06:46,380
Essentially, in this
[? Purdue ?] case

998
01:06:46,380 --> 01:06:47,420
is very simple.

999
01:06:47,420 --> 01:06:49,320
You first of all,
use the mean and then

1000
01:06:49,320 --> 01:06:50,900
you would adjust the deviation.

1001
01:06:50,900 --> 01:06:56,290
So therefore, given any
quantity X_0, you can have,

1002
01:06:56,290 --> 01:06:59,340
you can force it to
be any given mean.

1003
01:06:59,340 --> 01:07:01,830
This mean, in our case,
will be determined

1004
01:07:01,830 --> 01:07:03,645
by the martingale condition.

1005
01:07:08,390 --> 01:07:13,820
The next interesting thing
is martingale interpolation.

1006
01:07:13,820 --> 01:07:15,197
Oh, I have a typo here.

1007
01:07:20,470 --> 01:07:23,095
Sometimes you have an interest
rate model, for instance,

1008
01:07:23,095 --> 01:07:25,350
you model LIBOR.

1009
01:07:25,350 --> 01:07:28,995
Your LIBOR, you can
have different tenors.

1010
01:07:32,590 --> 01:07:35,639
When you have a yield curve,
you know, at any given time,

1011
01:07:35,639 --> 01:07:36,680
there's a term structure.

1012
01:07:39,280 --> 01:07:41,140
In the model, a
lot of times we can

1013
01:07:41,140 --> 01:07:44,290
model a few selected points.

1014
01:07:44,290 --> 01:07:48,410
But what if your model
requires a term structure,

1015
01:07:48,410 --> 01:07:51,720
a term that not in your model.

1016
01:07:51,720 --> 01:07:55,510
So what people normally
do is you do martingale,

1017
01:07:55,510 --> 01:07:58,290
you do interpolation.

1018
01:07:58,290 --> 01:08:02,425
So you have a 1-year LIBOR
and you have a 5-year liable.

1019
01:08:06,760 --> 01:08:08,455
And then you need a 3-years.

1020
01:08:08,455 --> 01:08:09,080
What do you do?

1021
01:08:09,080 --> 01:08:11,930
You interpolate, for instance.

1022
01:08:11,930 --> 01:08:14,950
But interpolation
doesn't automatically

1023
01:08:14,950 --> 01:08:19,819
guarantee martingale
relationships.

1024
01:08:19,819 --> 01:08:23,560
The martingale
interpolation has a goal

1025
01:08:23,560 --> 01:08:28,750
of automatically satisfying
the martingale relationships,

1026
01:08:28,750 --> 01:08:33,750
so we're particular
with our interpolating.

1027
01:08:33,750 --> 01:08:40,198
Actually, it turns out
to be a [INAUDIBLE]

1028
01:08:40,198 --> 01:08:45,180
The starting point is the
martingale condition that I

1029
01:08:45,180 --> 01:08:48,229
wrote out on the slide.

1030
01:08:48,229 --> 01:08:52,550
Essentially, this s and
t are the calendar time.

1031
01:08:52,550 --> 01:08:56,490
And this capital T is really
like a term structure.

1032
01:08:56,490 --> 01:09:00,080
You have a 1-year rate, 2-year
rate, 5-year interest rate,

1033
01:09:00,080 --> 01:09:01,203
those term structures.

1034
01:09:04,710 --> 01:09:09,600
How do we interpolate such
that after interpolation

1035
01:09:09,600 --> 01:09:14,319
the corresponding martingale
relationships are satisfied.

1036
01:09:14,319 --> 01:09:16,750
So here's what we do.

1037
01:09:16,750 --> 01:09:21,069
We start with, let's
say, capital T_1.

1038
01:09:24,100 --> 01:09:29,069
Capital T_1, that's
a point we model.

1039
01:09:29,069 --> 01:09:32,899
We assume that one is
properly martingale resampled

1040
01:09:32,899 --> 01:09:34,859
and satisfies the
martingale condition.

1041
01:09:37,370 --> 01:09:44,979
This is a martingale
for T capital 2.

1042
01:09:44,979 --> 01:09:49,240
That also satisfies the
corresponding martingale

1043
01:09:49,240 --> 01:09:50,149
conditions.

1044
01:09:50,149 --> 01:09:53,170
Our goal is to figure out T_3.

1045
01:09:53,170 --> 01:09:59,612
How do you do interpolation
for the term T_3

1046
01:09:59,612 --> 01:10:06,830
such that this T_3 will
satisfy its own corresponding

1047
01:10:06,830 --> 01:10:08,660
martingale condition.

1048
01:10:08,660 --> 01:10:11,600
If you do simple linear
interpolation using

1049
01:10:11,600 --> 01:10:19,100
T as independent
variable, essentially, you

1050
01:10:19,100 --> 01:10:22,230
are not going to achieve that.

1051
01:10:22,230 --> 01:10:28,830
So the key is we need the choose
the proper independent variable

1052
01:10:28,830 --> 01:10:30,350
for the interpolation.

1053
01:10:30,350 --> 01:10:36,695
Essentially, it's the previous
time or time 0 quantity.

1054
01:10:39,340 --> 01:10:42,540
So time s is before time t.

1055
01:10:42,540 --> 01:10:46,080
Imagine time s will be 0.

1056
01:10:46,080 --> 01:10:49,190
So using the
corresponding quantities

1057
01:10:49,190 --> 01:10:53,020
at time 0 as the
independent variable,

1058
01:10:53,020 --> 01:10:55,540
essentially, you
can achieve that.

1059
01:10:55,540 --> 01:10:57,600
It's still linear
interpolation, it's

1060
01:10:57,600 --> 01:11:01,870
just to use a different
independent variable.

1061
01:11:01,870 --> 01:11:04,280
Essentially, you can
show that very easily.

1062
01:11:04,280 --> 01:11:06,510
This is just simple algebra.

1063
01:11:06,510 --> 01:11:10,630
If you take the expectation,
this one being martingale,

1064
01:11:10,630 --> 01:11:13,950
this little t will become s.

1065
01:11:13,950 --> 01:11:17,490
Then if you do expectation
here, the little t

1066
01:11:17,490 --> 01:11:19,910
will become little s.

1067
01:11:19,910 --> 01:11:24,970
And therefore if you combine
these two, a lot of terms

1068
01:11:24,970 --> 01:11:28,460
will actually cancel.

1069
01:11:28,460 --> 01:11:34,440
Essentially, you will be
left with this martingale

1070
01:11:34,440 --> 01:11:44,280
at time s and T_3, meaning
this is the martingale target

1071
01:11:44,280 --> 01:11:47,850
of this particular term.

1072
01:11:47,850 --> 01:11:51,830
And that turns out to be the
expectation of this quantity.

1073
01:11:51,830 --> 01:11:55,000
So it's a very simple
linear-- simple algebra.

1074
01:11:55,000 --> 01:11:59,640
You guys can figure
it out if you want to.

1075
01:11:59,640 --> 01:12:04,380
So this one
essentially guarantees

1076
01:12:04,380 --> 01:12:07,190
the interpolated
quantity automatically

1077
01:12:07,190 --> 01:12:10,810
satisfies all the conditions
of the martingale target.

1078
01:12:10,810 --> 01:12:13,000
Of course, you need to
know the martingale target.

1079
01:12:13,000 --> 01:12:15,330
If you don't know,
that's a different story.

1080
01:12:15,330 --> 01:12:17,760
Then you need to
do something else.

1081
01:12:17,760 --> 01:12:20,480
Specifically, time
0, for instance,

1082
01:12:20,480 --> 01:12:22,550
is what the market tells us.

1083
01:12:25,450 --> 01:12:27,565
Often time we do a
big time assumption.

1084
01:12:27,565 --> 01:12:33,880
So whatever assumption on time 0
you make, in you dynamic model,

1085
01:12:33,880 --> 01:12:38,790
you automatically satisfy the
needed martingale condition.

1086
01:12:46,920 --> 01:12:49,860
This is just a
brief introduction

1087
01:12:49,860 --> 01:12:52,705
of how we do the
martingale modeling.

1088
01:12:56,490 --> 01:13:00,120
This LIBOR market model,
as you guys probably

1089
01:13:00,120 --> 01:13:03,380
have learned already,
there's different forms

1090
01:13:03,380 --> 01:13:05,540
of BGM as the initial form.

1091
01:13:05,540 --> 01:13:11,840
And then Jamshidian
came with another form.

1092
01:13:11,840 --> 01:13:15,230
And in terms of a
general martingale

1093
01:13:15,230 --> 01:13:17,920
model, what we'll
do typically is

1094
01:13:17,920 --> 01:13:23,320
we start to find the
martingale quantity.

1095
01:13:23,320 --> 01:13:27,770
And we know a forward
LIBOR is a martingale

1096
01:13:27,770 --> 01:13:32,440
in its own forward measure.

1097
01:13:32,440 --> 01:13:37,890
Then we know we can use
martingale representation.

1098
01:13:37,890 --> 01:13:42,350
Under certain
technical conditions,

1099
01:13:42,350 --> 01:13:47,990
the diffusion process can be
represented by Brownian motion.

1100
01:13:47,990 --> 01:13:50,850
Then we can assume
log-normal just for example.

1101
01:13:50,850 --> 01:13:52,910
We don't have to,
we can use CEV,

1102
01:13:52,910 --> 01:13:56,870
we can use [INAUDIBLE]
stochastic volatility.

1103
01:13:56,870 --> 01:13:59,000
The starting point
is martingale,

1104
01:13:59,000 --> 01:14:02,460
identifying the
martingale measure

1105
01:14:02,460 --> 01:14:04,780
and then perform
martingale representation.

1106
01:14:04,780 --> 01:14:08,605
Essentially, you get this
stochastic differential

1107
01:14:08,605 --> 01:14:10,670
equation.

1108
01:14:10,670 --> 01:14:15,820
They need to change measure
or change numeraire.

1109
01:14:15,820 --> 01:14:19,480
Because this one essentially
says for particular LIBOR,

1110
01:14:19,480 --> 01:14:23,240
you have a Brownian motion
and a different measure.

1111
01:14:23,240 --> 01:14:26,440
So that has limited usage.

1112
01:14:26,440 --> 01:14:29,270
A lot of the derivative
trade, IR trade

1113
01:14:29,270 --> 01:14:33,215
essentially, it's [INAUDIBLE]
the entire yield curve.

1114
01:14:33,215 --> 01:14:35,340
So you need to make sure
you model the entire yield

1115
01:14:35,340 --> 01:14:37,200
curve consistently.

1116
01:14:37,200 --> 01:14:41,760
So therefore you have to
change the probability measure

1117
01:14:41,760 --> 01:14:49,460
so that everything is specified
in the same common measure.

1118
01:14:53,454 --> 01:14:55,370
Of course, you can have
a choice which one you

1119
01:14:55,370 --> 01:14:59,490
want to use as common measure.

1120
01:14:59,490 --> 01:15:03,020
Through a simple
change of numeraire,

1121
01:15:03,020 --> 01:15:06,900
essentially, we can get a
stochastic equation like this.

1122
01:15:21,580 --> 01:15:23,550
We have a Brownian motion.

1123
01:15:33,670 --> 01:15:39,270
Right, we have a Brownian motion
with a correlation like this.

1124
01:15:47,470 --> 01:15:54,580
So this is essentially a
market model in a general form,

1125
01:15:54,580 --> 01:16:00,850
with full dimensionality
meaning one Brownian motion

1126
01:16:00,850 --> 01:16:03,724
per term of a LIBOR.

1127
01:16:03,724 --> 01:16:05,140
So that's the full
dimensionality.

1128
01:16:05,140 --> 01:16:05,723
PROFESSOR: Yi?

1129
01:16:05,723 --> 01:16:09,490
YI TANG: And then you
need to do-- Yeah, hi.

1130
01:16:09,490 --> 01:16:14,470
PROFESSOR: Can you wrap up
because we need a bit of time

1131
01:16:14,470 --> 01:16:15,169
for questions.

1132
01:16:15,169 --> 01:16:16,460
YI TANG: Oh you need me to end.

1133
01:16:16,460 --> 01:16:21,010
It's all right I can
actually wrap up now.

1134
01:16:21,010 --> 01:16:22,950
If you want to.

1135
01:16:22,950 --> 01:16:24,930
PROFESSOR: Sure.

1136
01:16:24,930 --> 01:16:28,680
OK, any conclusions?

1137
01:16:28,680 --> 01:16:30,070
YI TANG: Well, OK.

1138
01:16:30,070 --> 01:16:34,130
The conclusion is
the following thing.

1139
01:16:34,130 --> 01:16:37,850
There is a need for
enterprise-level models

1140
01:16:37,850 --> 01:16:40,190
to handle non-linear
portfolio effects

1141
01:16:40,190 --> 01:16:43,740
and we need to leverage
our trade-level models.

1142
01:16:43,740 --> 01:16:47,600
By doing so we do employ
martingale testing,

1143
01:16:47,600 --> 01:16:50,880
martingale resampling,
interpolation.

1144
01:16:50,880 --> 01:16:54,670
And not only we
need that for CVA,

1145
01:16:54,670 --> 01:16:58,230
but we also need that for
funding liquidity capital risks

1146
01:16:58,230 --> 01:17:00,580
which are very critical risks.

1147
01:17:00,580 --> 01:17:04,010
And people have started
paying more and more attention

1148
01:17:04,010 --> 01:17:09,020
to these risks, especially
since after the crisis.

1149
01:17:09,020 --> 01:17:11,170
Because of time
limits, I'm not going

1150
01:17:11,170 --> 01:17:13,020
to be able to finish
another example.

1151
01:17:13,020 --> 01:17:18,220
But if you like, you can take a
look on page 22 of the slides.

1152
01:17:18,220 --> 01:17:21,090
Hopefully, Vasily can
still get it to you guys.

1153
01:17:21,090 --> 01:17:22,860
Thank you guys.

1154
01:17:22,860 --> 01:17:26,126
PROFESSOR: Thank you Yi.

1155
01:17:26,126 --> 01:17:28,890
We will publish the slides
probably later tonight

1156
01:17:28,890 --> 01:17:32,360
so please take a look.

1157
01:17:32,360 --> 01:17:35,960
So to wrap up, let me see.

1158
01:17:35,960 --> 01:17:37,442
I want to bring up,

1159
01:17:37,442 --> 01:17:38,400
PROFESSOR 2: That's OK.

1160
01:17:38,400 --> 01:17:41,330
Probably if it's the course
website, that's fine.

1161
01:17:44,770 --> 01:17:47,500
PROFESSOR: I did add
a few topics which

1162
01:17:47,500 --> 01:17:50,990
were used last year for
final paper for interest

1163
01:17:50,990 --> 01:17:53,250
in the document which
is on the website.

1164
01:17:53,250 --> 01:17:56,340
So take a look.

1165
01:17:56,340 --> 01:18:05,060
Basically, the themes there were
mostly Black-Scholes or more

1166
01:18:05,060 --> 01:18:09,290
advanced models or manipulation
of Black-Scholes equation.

1167
01:18:09,290 --> 01:18:12,260
There was a very interesting
work on statistical analysis

1168
01:18:12,260 --> 01:18:14,730
of commodity data.

1169
01:18:14,730 --> 01:18:20,030
So if somebody's up for it,
that would be very interesting.

1170
01:18:20,030 --> 01:18:29,200
And there were a few numerical
and Monte Carlo projects.

1171
01:18:29,200 --> 01:18:32,180
So any questions?

1172
01:18:32,180 --> 01:18:34,702
PROFESSOR 2: Yeah,
so actually we

1173
01:18:34,702 --> 01:18:36,410
were planning to give
you a bit more time

1174
01:18:36,410 --> 01:18:38,460
to ask your questions.

1175
01:18:38,460 --> 01:18:41,050
But since we have
five minutes, I

1176
01:18:41,050 --> 01:18:45,320
think maybe I'd like to ask
you to just think about what

1177
01:18:45,320 --> 01:18:47,540
we learned this term.

1178
01:18:47,540 --> 01:18:50,950
So Peter can add
on what we think

1179
01:18:50,950 --> 01:18:54,340
in on the mathematics and
also those applications,

1180
01:18:54,340 --> 01:18:58,940
and in conjunction while you're
doing the final paper, just

1181
01:18:58,940 --> 01:19:02,340
focusing on the new things
you think that you learned

1182
01:19:02,340 --> 01:19:07,520
and what did you like to
explore in the next stage

1183
01:19:07,520 --> 01:19:09,610
of your research.

1184
01:19:09,610 --> 01:19:12,750
So I think probably we
don't have a lot of time

1185
01:19:12,750 --> 01:19:14,782
for lots of questions.

1186
01:19:14,782 --> 01:19:16,240
But if you have
any questions, this

1187
01:19:16,240 --> 01:19:17,615
will be a good
opportunity to ask

1188
01:19:17,615 --> 01:19:19,480
about the paper or the course.

1189
01:19:19,480 --> 01:19:21,243
Peter you want to
make some comments?

1190
01:19:21,243 --> 01:19:22,010
PETER: Sure.

1191
01:19:22,010 --> 01:19:24,810
I'd just like say that
I think this course was

1192
01:19:24,810 --> 01:19:28,230
a very challenging course
for most of you and that was,

1193
01:19:28,230 --> 01:19:29,260
I guess, our intention.

1194
01:19:29,260 --> 01:19:32,610
And I really respect all
the hard work and effort

1195
01:19:32,610 --> 01:19:34,310
everyone put into the class.

1196
01:19:34,310 --> 01:19:37,910
And in terms of
the final paper, we

1197
01:19:37,910 --> 01:19:40,630
will be looking
at your background

1198
01:19:40,630 --> 01:19:45,850
and look for insights
that demonstrate what

1199
01:19:45,850 --> 01:19:47,340
you've learned in the course.

1200
01:19:47,340 --> 01:19:51,404
And I've already
reviewed several papers.

1201
01:19:51,404 --> 01:19:52,820
I'm very pleased
with the results.

1202
01:19:52,820 --> 01:19:56,130
So I think everyone's
done a great job.

1203
01:19:56,130 --> 01:19:59,490
This course, I
think, is intended

1204
01:19:59,490 --> 01:20:01,170
to provide you with
the foundations

1205
01:20:01,170 --> 01:20:04,280
of the math for the financial
applications as well

1206
01:20:04,280 --> 01:20:09,540
as an excellent introduction and
exposure to those applications.

1207
01:20:09,540 --> 01:20:14,090
I think you'll find this
course valuable over the course

1208
01:20:14,090 --> 01:20:17,310
of your careers,
and look forward

1209
01:20:17,310 --> 01:20:22,460
to contributing
insights with questions

1210
01:20:22,460 --> 01:20:23,960
you might have
following the course.

1211
01:20:23,960 --> 01:20:26,540
I'm sure the other
faculty feel the same way.

1212
01:20:26,540 --> 01:20:30,579
We want to be a good resource
for you now and afterwards.

1213
01:20:30,579 --> 01:20:31,870
PROFESSOR: Very, very well put.

1214
01:20:31,870 --> 01:20:35,240
So please feel
free to contact us.

1215
01:20:35,240 --> 01:20:38,320
And please stay in touch.

1216
01:20:38,320 --> 01:20:42,720
All the contact details
are on the website.

1217
01:20:42,720 --> 01:20:45,970
We plan to have a repeat
of this class next year.

1218
01:20:45,970 --> 01:20:49,440
So please, tell your friend
or stop by next year,

1219
01:20:49,440 --> 01:20:51,780
which will be the next fall.

1220
01:20:51,780 --> 01:20:54,820
It will not be exactly the same.

1221
01:20:54,820 --> 01:20:57,120
We will try to make
it slightly different,

1222
01:20:57,120 --> 01:20:58,260
but it will be close.

1223
01:20:58,260 --> 01:21:00,410
PROFESSOR 2: If you have
any suggested topics,

1224
01:21:00,410 --> 01:21:02,410
you feel you haven't
been exposed to

1225
01:21:02,410 --> 01:21:06,640
and would like to know more,
send us email if you can.

1226
01:21:06,640 --> 01:21:08,750
I think one of the
values of this class

1227
01:21:08,750 --> 01:21:12,276
is we can bring in
pretty much everyone

1228
01:21:12,276 --> 01:21:14,960
from the frontier
in this industry

1229
01:21:14,960 --> 01:21:18,460
to give you some insights
of what's going on.

1230
01:21:18,460 --> 01:21:22,120
PROFESSOR: Please take
a review on the website,

1231
01:21:22,120 --> 01:21:22,930
this is important.

1232
01:21:26,040 --> 01:21:27,734
And that's all.

1233
01:21:27,734 --> 01:21:28,400
PROFESSOR 2: OK.

1234
01:21:28,400 --> 01:21:30,650
Thank you for your
participation this semester.

1235
01:21:30,650 --> 01:21:32,450
[APPLAUSE]

1236
01:21:32,450 --> 01:21:35,200
PROFESSOR: And thank
Yi for the pleasure.