MATH 168 A: INTRODUCTION TO NUMERICAL METHODS IN FINANCE (SPRING 2000)

**Lecture Time: **To be announced. **Lecture Place: **To be announced.

**Professor: **Professor H. B. Sieburg

**DESCRIPTION: **This course is an introduction to the numerical mathematics of financial models. The aim is to provide students with an overview of the basic computational tools and associated mathematical machinery that are used by financial analysts and financial engineers today. To this avail, the course will combine a streamlined introduction to finite differences, Monte Carlo simulation, linear programming, and trees with case studies of actual portfolio and risk management decisions made by money managers in the security and derivative markets. Numerical experiments will be conducted using Microsoft Excel spreadsheets with occasionally embedded *Mathematica* code (knowledge of the Mathematica programming environment is not required for this course as we shall introduce the concepts as needed; prior knowledge of MS Excel may be useful).

**PREREQUISITES: **Math 20D, Math 20F, and Math 194.

**TEXT: **__P. Wilmott et al.__, The Mathematics of Financial Derivatives, Cambridge University Press, 1995. *This text will be used as a primary reference for the course. The lectures will provide a guide and expanded explanation of the relevant topics. *

**OTHER REFERENCES: **__S. Pliska__, Introduction to Mathematical Finance: Discrete Time Models, Blackwell, third printing, 1999. __W. Shaw__, Modelling Financial Derivatives with *Mathematica*. Cambridge University Press, First Edition, 1998. __E. Elton, M. Gruber__, Modern Portfolio Theory and Investment Analysis. Wiley & Sons, Fifth Edition, 1995. __S. Benninga__, Numerical Techniques in Finance. MIT Press, Second Edition, 1989. __R. Ibbotson, R. Sinquefield__, Stocks, Bonds, Bills, and Inflation: Historical Returns (1926-1987). The Research Foundation of The Institute of Chartered Financial Analysts, First Edition, 1989. __E. Thorp__, Beat the Market. Random House, First Edition, 1967.

**OUTLINE: **"Risk" and "Return" are THE keywords any investor, individual or institutional, lives by. Classical portfolio theory examines risk/return tradeoffs from a "mean-variance" framework. Here, the "risk" of an individual security is encapsulated by the variance (or, equivalently, standard deviation) of its returns. The higher the variance, the more uncertain the return, and therefore the greater the risk. The present course will briefly address the benefits of assembling a portfolio of securities to manage risk. Next, we shall discuss "hedging". "Hedging" is the process of reducing or eliminating a particular risk in a portfolio through a trade, a series of trades, or contractual agreements. We shall discuss a number of numerical methods currently in use for constructing "immunization" and "insurance" hedges using bonds and options. Finally, we shall address derivative pricing. In other words, we shall seek answers to the question of "How much is it worth to me to replicate a portfolio with a specific return, but with certain risks eliminated?". Throughout the course, real-life cases from the financial, oil, and drug industries will be discussed to illustrate the need for, and the efficiency of, numerical mathematics in the contest of corporate financial management.

**LINKS TO RELATED WEB SITES (under construction):**

Please direct any questions to Professor Hans B. Sieburg, email: hsieburg@ucsd.edu