Math-544. Computational Finance.

The teaching material presented below may change from semester to semester.

Instructor: Professor Vladimir Rotar; Office GMSE-514, phone: 594 7244; e-mail: rotar@sciences.sdsu.edu

or vrotar@euclid.ucsd.edu.

The course concerns financial markets and deals, in particular, with such notions as

· Stock prices;

· Pricing of options, forwards, etc;

· Portfolio selection and optimal behavior in the financial market;

· Analysis of financial markets.

To establish optimal trading or investment strategies we consider general aspects of

· Comparison of risky alternatives, the modern utility theory.

However, the emphasis in the course is on

computational techniques, analysis of real data, and numerical procedures for evaluating prices, optimal portfolios, etc., in situations when the analytical analysis is intractable.

The prerequisite is ordinary calculus (not complicated, but a student should be able, for example, to differentiate simple functions, and to know what the number e is), and an introductory course of Probability Theory (say, Stat-550 or Stat-551a are more than enough).

The course is self-contained; in particular Math-580, or Math-581 are NOT needed, though people who already have taken these courses are strongly recommended to complete the financial series taking this course too.

List of Topics.

1. Introduction. Comparison of risky alternatives: the classical utility theory; some aspects of the modern theory.

2. Expected utility maximization in the one-period framework, and in the dynamic model. Computational aspects of dynamic programming.

3. Statistics of financial processes. How to estimate drift and volatility.

4. A technique for pricing of derivative securities, in particular, options. Work with software.

5. Hedging strategies. Computational work with particular data.

6. Analysis of the financial market. Evaluation of typical characteristics.

7. The Monte Carlo Method, and its application in security pricing. Variance reduction.

References:

No book is suggested as a mandatory text-book. We use different sources, in particular, readers and handouts. Most of topics may be found in the following books.

1. Hull, John C. Options, Futures and Other Derivatives. 6th edition, 2006, Prentice-Hall.

2. Stampfli J., Goodman V. The Mathematics of Finance, Brooks/Cole, 2001.

3. Financial Economics, Ed. Panjer, 1998, The Actuarial Foundation.

4. V.I. Rotar, Actuarial Models, Chapman& Hall/CRC, 2006.

1. Boyle, P., Broadie, M., Glasserman, P. Monte Carlo methods for security pricing, J. of Economic dynamics and Control, 21 (1997)

2. Beninga, S. Financial Modelling, 2^nd edition, The MIT Press, 2000.