Math 339, Topics in Applied Mathematics

Spring 2007: Mathematical Finance

Tentative Syllabus

Topic Reading
Introduction to the course -
The motion of stock prices "Guide to Money and Investing" chapter on stocks
Return, logarithmic return -
Present and future value -
Rick-free assets; discrete and continuous compound interest -
Sample mean, variance, standard deviation, confidence intervals -
Random variables, expectation, variance -
Normal distribution -
Brownian motion as limit of coin tossing (random walk). Geometric Brownian motion -
Normality and independence of returns as a consequence of GBM -
Tests for normality: KS test, qq-plot -
Covarience, correlation -
Tests for independence: scatterplot, sample correlation coefficient -
Market portfolio, indices (eg Dow-Jones, S&P 500) -
Forwards Hull 1.3
Futures Hull 1.4
Introduction to options: long and short european puts and calls Hull 1.5
Bachelier (payoff) diagrams -
Put-call parity Hull 9.4
One-step binomial tree Hull Ch. 11
Risk-neutral valuation Hull 11.2
Multi-step binomial trees -
Black-Scholes formula Hull 13.8
Stochastic calculus, Ito's lemma Hull 13.5
Black-Scholes PDE Hull 13.6
American options, evaluation with a tree Hull 11.5
Implied volatility, volatility smile Hull 13.11
Exotic options Hull Ch. 22
Monte Carlo methods for pricing options -
Bonds -
Models of the interest rate. -

Time permitting

Topic Reading
Mean-variance optimization, efficient frontier -
Regression -
Capital asset pricing model, beta -