### Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session

### Course Description

This course covers the main quantitative methods of finance. The course covers three broad sets of topics: derivative pricing using stochastic calculus, dynamic optimization, and financial econometrics. The emphasis is on rigorous and in-depth development of the key techniques and their application to practical problems.

### Prerequisites

*15.401 Finance Theory I* is a prerequisite for this course. *15.437 Options and Futures Markets* is a recommended co-requisite.

Rudimentary programming skills are necessary. Homework assignments involve computer implementation of quantitative methods in MATLAB®. Prior knowledge of MATLAB® is not required. In addition to formal prerequisites, the course assumes solid undergraduate-level background in calculus, probability, and statistics.

### Grading

ACTIVITIES | PERCENTAGES |
---|---|

Group problem sets (6 total) | 50% |

Final exam | 50% |

### Course Textbooks

[Back]= Back, Kerry. *A Course in Derivative Securities:* *Introduction to Theory and Computation*. New York, NY: Springer, 2005. ISBN: 9783540253730.

[CL&M]= Campbell, John Y., Andrew W. Lo, and A. Craig MacKinlay. *The Econometrics of Financial Markets*. Princeton, NJ: Princeton University Press, 1996. ISBN: 9780691043012.

[Cochrane]= Cochrane, John H. *Asset Pricing*. Revised ed. Princeton, NJ: Princeton University Press, 2005. ISBN: 9780691121376.

[D&S]= DeGroot, Morris, and Mark J. Schervish. *Probability and Statistics*. 3rd ed. Reading, MA: Addison-Wesley, 2002. ISBN: 9780201524888.

[Tsay]= Tsay, Ruey S. *Analysis of Financial Time Series*. 2nd ed. New York, NY: John Wiley & Sons, 2005. ISBN: 978047169074.

The lectures will include suggestions for additional readings for each topic. Since there is no single textbook covering all the relevant topics, several books will be used. [Back] covers topics in stochastic calculus and derivative pricing. [Tsay] covers time-series methods in financial econometrics, and is the most frequently used textbook. [Cochrane] and [CL&M] cover advanced topics in financial econometrics. [D&S] covers basic background in probability and statistics and can be used for review as necessary.

### List of Topics

The class will cover the following core topics:

- Absence of arbitrage and risk-neutral pricing;
- Itô stochastic calculus, Black-Scholes model and extensions, interest rate models;
- Dynamic programming, asset allocation, Merton’s solution, numerical methods for dynamic portfolio choice;
- Monte Carlo simulation for derivative pricing;
- Maximum likelihood and quasi-maximum likelihood estimation;
- Generalized method of moments (GMM) basics, regression as GMM, standard errors, delta-method;
- Small-sample inference, bootstrap;
- Volatility models, GARCH.

Advanced topics include:

- Derivative pricing and dynamic portfolio choice;
- Extensions of GARCH, MIDAS models, multivariate volatility models;
- Exploiting return predictability.

### Calendar

WEEK # | KEY DATES |
---|---|

1 | |

2 | |

3 | Problem set 1 due |

4 | |

5 | Problem set 2 due |

6 | Problem set 3 due |

7 | |

8 | |

9 | Problem set 4 due |

10 | |

11 | Problem set 5 due |

12 | |

13 | Problem set 6 due |

14 | |

15 |