Math 586 - Computational Financial

Spring Semester 2007

Meetings: MWF 12:00-1:00 -- Taft 219 (NOTE CHANGE)

Call Number: 16494

Instructor: Charles Tier - e-mail: tier@uic.edu

Office: 720 SEO, 6-2442, office hours 1-2 MW or apt.

The course will present current topics in computational finance emphasizing the pricing of financial derivatives such as stock options and fixed income derivatives. The stress will be on the construction and computation of the derivative prices. This will involve the solution of stochastic differential equations and their related partial differential equations. Analytic methods will introdcued and used to construct pricing formulas, if possible. Numerical methods, based on Matlab, will be presented and used to analyze both data and analytically intractable models.

Student background: students should be familiar with basic probability, differential equations and elementary numerical methods.

Topics:

1. Introduction to derivatives - interest rates, forward and future contracts; European and American stock options, combinations to options, replication of contracts, valuations and profit and loss curves, arbitrage and the principle of non-arbitrage pricing.

2. Random behavior of assets: historical data, return statistics.

3. Stochastic Differential Equations - what are they, how to solve, relationship to partial differential equations.

4. Option Pricing Models - derivation, integral and differential equation formulations, theories of Bachelier, Black-Scholes, and Merton.

5. Brief review of partial differential equations; backward and forward diffusion equations, analytic solution of Black-Scholes model; free boundary value problem for pricing American options, similarity solutions

6. Numerical solution of partial differential equations arising in pricing models; binomial trees, finite difference methods - explicit and implicit, Crank-Nicholson, methods for American options.

7. Interest rate models - yield curves, FRA, Swaps, short rate models, bond pricing, calibration, caps, swaptions

Text:

Useful Reference:

Desmond Higham, An Introduction to Financial Option Valuation, Cambridge, 2004 - Excellent Matlab reference.

References on Reserve in Main Library
• Lipton, Mathematical Methods for Foreign Exchange, World Scientific, 2001.
• Wilmott, Mathematics of Financial Derivatives, Student Intro
• Neftci, An Introduction to the Mathematics of Financial Derivatives
• Baxter and Rennie, Financial Calculus
• Hull, Options, Futures, and Derivatives

Grading: The course grade will be based on homework problems, computer projects, and possibly one in class quiz. Matlab will be the basic computational tool for the computer projects and, is available on all UIC lab computers.

URL:

by Charles Tier