Math 203, Mathematical Tools for Finance
Not offered in 2005-06

Over the past two decades, new quantitative techniques have transformed the investment process and the finance industry. Today, banks and other financial institutions gain competitive advantage through technical innovation. Powerful models based on diverse mathematical techniques and finance theory predict returns, measure risk, and value complicated transactions. Computational methods transform these theories into tools that sit at the fingertips of traders, portfolio managers, regulators, and risk managers, bringing greater efficiency and rigor to financial markets. These developments have led to a large and growing demand for talented people trained in the mathematics of finance.

Math 203 is designed as an introductory course for students in mathematical finance. Although the mathematical aspects of the course are quite demanding, the course would be an excellent choice for students who are interested in quantitative techniques in financial applications. The main topic is the theory of options. The following is a collection of sample problems that appeared in a midterm exam for the class, Fall 1999.

Sample exam problems.

1. Write the stochastic differential equation for the asset price S. State Ito's lemma for f(S, t). Explain the meaning of each variable and coefficient in these two equations. Find the stochastic differential equation satisfied by f(S, t)= Sln (t+1).

2. Explain carefully the difference between writing a call option and buying a put option. What is the difference between a European option and an American option? If a trader buys a European call option and sells a European put option for the same underlying asset, with the same strike price and maturity date, describe the trader's position and draw the payoff diagram.

3. (a) A trader buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the trader make a profit? Under what circumstances will the option be exercised? Draw a diagram.

(b) Same question as above, but the trader sells a European call on a share for $4, the stock price is $47 and the strike price is $50.

4. Draw the expiry payoff diagram for the following portfolio: long one call with exercise price E, short one call and long one put with the same exercise price F. Assume that E < F.

Prerequisite: 116 or the equivalent.
Distribution: Mathematical Modeling

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