Lecture Notes

Code for related simulations and models are available with the lecture notes, some of which may be useful on the Problem Sets.

1 Arbitrage-free pricing models (PDF - 1.1MB)

Stochastic calculus and option pricing

Code: Quadratic variation simulation




Simulation methods

Code: Black-Scholes model Monte Carlo illustration

Code: Black-Scholes with a jump Monte Carlo (PS1, Q2)

Code: Monte Carlo with control variates, stochastic volatility model





4 Dynamic portfolio choice I: Static approach to dynamic portfolio choice (PDF)
5 Dynamic portfolio choice II: Dynamic programming (PDF)

Dynamic portfolio choice III: Numerical approximations in dynamic programming

Code: Numerical DP solution



7 Parameter estimation (PDF)
8 Standard errors and tests (PDF)
9 Small-sample inference and bootstrap (PDF)
10 Volatility models (PDF)
11 Review: Arbitrage-free pricing and stochastic calculus (PDF)
12 Review: DP and econometrics (PDF)

The following handouts and slides were used to supplement lecture materials.

Crossing probabilities of the Brownian motion (PDF)

Key points: Derivatives and Monte Carlo (PDF)

Dynamic programming: Justification of the principle of optimality (PDF)

Examples of dynamic programming problems (PDF)