Math 4226 Course Outline

Course Content

I- Introductory Derivatives: Forwards and Futures.

II- General Properties of Options.

III- Binomial Pricing Models.

IV- Black-Scholes Option Pricing Model.

V- Option Greeks and Risk Management.

Specific topics per week:

Week 1: Introduction to derivatives, forwards, synthetic forwards.

Week 2: Prepaid forwards, futures, call and put options.

Week 3: Option strategies, synthetic options.

Week 4: Contract combinations: bear spreads, bull spreads, collars, straddles, strangles, and butterfly spreads.

Week 5: Put-call parity with stocks and currencies, bounds for option prices.

Week 6: Early-exercise of American options, time-to-expiry.

Week 7: Comparing options with different strikes: monotonicity, slope and convexity properties. Midterm Exam.

Week 8: Binomial tress- stock, one period; risk-neutral pricing; replicating portfolio.

Week 9: Volatility; pricing European options on stocks and currencies and American options using multi-period binomial trees.

Week 10: Modeling stock prices with the lognormal distribution; conditional payoffs.

Week 11: Black-Scholes formula for stock, currency and options on futures; Greeks.

Week 12: Delta-hedging: overnight profit, the delta-gamma-theta approximation, hedging multiple Greeks.

Week 13: Asian and barrier options.

Week 14: Compound, gap, and exchange options.

Week 15: Actuarial applications of options.

Week 16: Review, Final Exam.