### Lecture Information

Instructor: Adam Bowers

Time: 12:00-12:50 pm (MWF)

Location: CSB 001

TA Name |
Section |
Time (Thu) |
Location |
Office Hours |
---|---|---|---|---|

Benjamin Greenberg | A1 | 2 pm | APM 5402 | Week 10 Hours: W 2-4 in APM 6436 |

Bob Chen | A2 | 3 pm | APM 5402 | (No week 10 hours) |

A3 | 4 pm |

**COURSE DESCRIPTION:**
This course provides an introduction to the mathematics of some financial models. The aim is to provide students with an introduction to some basic probabilistic models of finance and associated mathematical machinery. The course focuses largely on financial derivatives and related mathematics.

The course begins with the development of the basic ideas of hedging and pricing of derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. The famous Black-Scholes option pricing formula is derived as a limit from these models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all introduced and used in this discrete setting.

This course requires a solid background in probability, preferably at the level of the undergraduate probability course Math 180A at UCSD. It also uses a certain amount of geometric linear algebra, so it is a good idea to review background from Math 20F.

The graduate course, Math 294, which has a similar title, is at a more advanced level and has much more emphasis on continuous time models which use measure theory.

**TEXT:** Introduction to the Mathematics of Finance, R. J. Williams, American Mathematical Society, 2006.

We will cover the first three chapters of the book.

**OTHER REFERENCES:**

F. AitSahlia and K. L. Chung, **Elementary Probability Theory**, Springer, Fourth Edition.

M. Capinski and T. Zastawniak, **Mathematics for finance: an introduction to financial engineering**, Springer, 2010.

J. Cvitanic and F. Zapatero, **Economics and Mathematics of Financial Markets**, MIT Press, 2004.

T. S. Y. Ho and S. B. Lee, **The Oxford Guide to Financial Modeling**, Oxford, 2004.

J. Hull, **Options, Futures and Other Derivative Securities**, Prentice Hall.

S. Pliska, **Introduction to Mathematical Finance**, Blackwell, 1998.

S. Ross, **An Introduction to Mathematical Finance, Options and Other Topics**, Cambridge University Press, 1999.

J. Stampfli and V. Goodman, **The Mathematics of Finance: Modeling and Hedging**, AMS, 2001.

P. Wilmott et al., **The Mathematics of Financial Derivatives**, Cambridge University Press, 1995.

Incomplete Markets by Jeremy Staum, article in **Handbooks in OR and MS**, Vol. 15, 2008, Elsevier.

**OTHER RESOURCES:**

Linear algebra lectures by Gil Strang (MIT). You may find lecture 1, 9, 14 helpful in reviewing geometric aspects of linear algebra.

**WIKEPEDIA AND OTHER LINKS: **

- Forward contracts
- Futures contracts
- Options
- Swaps
- Credit Default Swaps
- Scholes-Merton Nobel Prize citation, 1997.
- Myron Scholes' Nobel Lecture, 1997.
- Robert Merton's Nobel Lecture, 1997.
- An article by Marsh and Kobayashi on the Contributions of Black, Merton and Scholes to the financial services industry, June 2001.
- Darrell Duffie's website with articles on various financial market policy issues
- Article by Jeremy Kress in Harvard Journal on Legislation, 2011, related to clearinghouses for swaps.

**NEWS ARTICLES:**

- Don't Blame the Quants, by Steven Shreve, Forbes Magazine, October 2008.
- "The End of the Financial World as We Know It" and "How to Repair a Broken Financial World", by Michael Lewis and David Einhorn, New York Times, Jan 4, 2009.
- Capitalist Fools, by Joseph Stiglitz, January 2009, Vanity Fair.
- After Sure-Bet Investment Fails, a Bank Contends It Was Duped, by Vikas Bajaj, New York Times, January 20, 2009.
- Obama plans fast action to tighten financial rules, by Stephen Labaton, New York Times, January 25, 2009.
- Time to unravel the knot of credit default swaps, by Gretchen Morgenson, New York Times, January 25, 2009.
- Six errors on the path to the financial crisis, by Alan S. Blinder, New York Times, January 25, 2009.
- NPR "This American Life" Program on the subprime mortgage crisis.
- New York Times Article about current use of credit default swaps, January 30, 2012.

**Course description, list of references, and other resources provided by Professor Ruth Williams.**