This is the first time this course is being run. This syllabus
represents our wish list. We will adjust the pace, as we see how it
proceeds.

It may be that we do not cover
the last few topics.

**WEEK 1:**Introduction to financial markets and derivatives. Ideas of replication and no arbitrage pricing for forward contracts and the one-period model. Probability review.

**Text:**Sections 1.2---1.3, 2.1, 2.1. Class notes.**WEEK 2:**Risk neutral measure, pricing and the fundamental theorem of asset pricing for the one period model.

**Text:**Sections 2.2, 2.3, 2.5. Class notes.-
**WEEK 3:**Multi-period, binomial tree models, I: Pricing European options by backward induction.

**Text:**Sections 3.1, 3.2, 4.1, 4.2. Class notes. -
**WEEK 4:**Multi-period binomial tree models, II; Risk neutral measure and conditional expectation price formulas; Asian option. Fundamental theorem of asset pricing and martingales.

**Text:**Section 3.3 and class notes. **WEEK 5:**Multi-period binomial tree models, III; pricing American and exotic options.

**Text:**Sections 3.2, 3.3, 4.3.-
**WEEK 6:**Continuous time models: Central limit theorem and limit of

binomial trees. Brownian motion and geometric Brownian motion.

**Text:**Sections 5.1 and 5.2. -
**WEEK 7:**The Black-Scholes model and the Black-Scholes pricing formula.

**Text:**Sections 5.4 and 5.5. -
**WEEK 8:**Analytic approach to Black-Scholes: Stochastic differentials, Ito's rule, continuous time martingales.

**Text:**Sections 6.1---6.4. **WEEK 9:**The partial differential equation approach to pricing. Application to other options.

**Text:**Sections 6.5 and 6.6.**WEEK 10:**Hedging: delta and the other greeks.

**Text:**Chapter 7.**WEEK 11:**Interest rates: forward rates, zer0-coupon bonds, swaps.

**Text:**Sections 8.1-8.3.**WEEK 12:**Interest rate models in discrete time and pricing.

**Text:**Sections 8.4 and 8.5**WEEK 13:**Interest rate models in discrete and continuous time and pricing.

**Text:**Sections 8.5 and 8.6.**WEEK 14:**Computational methods for bonds.

**Text:**Sections 9.1 and 9.2.