This course is a continuation from the fall semester; however, it is open to new participants having the background mentioned below. New participants should check with the instructor at petrie@rci.rutgers.edu. The course is currently scheduled for TF3. That may be flexible. Check with instructor.

This course is an introduction to the field of financial mathematics. One of the chief aims is to provide the theoritical framework in which to value securities especially derivative securities. (Basic securities are stocks and bonds. A derivative security is any security whose value is derived from a basic security. Examples are stock indicies, options and futures.) Another aim is to provide the mathematical tools and develop mathematical models which will lead to valuation of securities and to trading and hedging strategies. Another aim of the course is to provide the framework to evaluate and manage risk in holding securities.

The course will begin with a discussion of the financial aspects of the course. This involves definitions of various securities and the details and operation of the markets in which they trade. Here are some examples: Forward and Future Contracts. Future Markets and Hedging, Options, Swaps, Leaps.

The central mathematical feature of this field concerns modeling the individual markets mathematically. Serious work in this area requires applied propability, statistics, some computer skills and stochastic partial differential equations. This material will be developed in the course. For background, participants should have some probability background like a good undergraduate course in probability and or statistics and some ability with a computer such as connecting to the internet and downloading files. Excel is an important computer skill which is often used in practical applications.

Any model in this area begins with some probability assumptions. The valuations which occur may come from probabilitic arguments or equilibria arguments. Both approaches will be discussed. A famous example of this is the derivation of the Black-Scholes formula for the price of a European Option. We will treat the model for this and the derivation in detail from both points of view. In the same spirit we will also treat other securities mentioned above in the same light. A basic tool in managing risk is the Capital Asset Pricing Model. This too will be treated.

In addition to presenting the theory behind the models and pricing of financial assets, we will present trading strategies for buying and selling stocks and bonds. We will present statistical tests for evaluating the trading strategies and we will emperically evaluate the trading strategies using current data available on the internet using an excel based program.

For further information about the course including registration, please contact Professor Petrie by email at petrie@rci.rutgers.edu.

Refs: Options, Futures and Other Derivative Securities by J. Hull ; An introduction to probability and its applications vols. I and II by W. Feller; Arbitrage Pricing-notes by Musiela and Rutkowski. The Econometrics of Financial Markets by Campbell et. al.