1. Final Review

2. Basic Derivatives Options –Non-linear Payoffs Futures and Forward Contracts –Linear Payoffs

3. No-Arbitrage Principle Model independent results – –An American call option on a non-dividend payment should never be exercised early. –Put-Call Parity Model dependent results –Put-Call Symmetry

4. The Black-Scholes Model The underlying asset is a traded asset GBM assumptions Delta hedging and no-arbitrage principle

5. Binomial Tree Method A discrete model. Consistency between BTM and PDE

6. Linkage between PDE and Expectation V(S,t)=exp(-r*(T-t))*E[max(S(T)-X,0)|S(t)=S] where

7. Three Methods PDE BTM Monte-Carlo Simulation

8. Exotic Options Under the Black-Scholes framework. American style Multi-asset options (multi-dimensional Ito lemma) Barrier options Asian options and lookback options Shouting options Forward start options Compound options

9. Similarity Reduction PDE BTM

10. Beyond Black-Scholes Implied volatility and volatility smile phenomenon Improved model: –Local Vol –Stochastic Vol –Jump-diffusion This Chapter is not required

11. The Risk Neutral Valuation Traded asset Non-traded underlying –Stochastic volatility model –Short rate model

12. Interest Rate Model Spot rate model (short-term rate model) –Yield curve fitting HJM model

13. One Topic Not Discussed Credit risks and derivatives –P.J. Schonbucher (2003) Credit Derivatives Pricing Models: models, pricing and implementation, John Wiley & Sons Ltd.

14. Concerning the Final Exam Time: 9:00am-11:30am on 26 Nov (Monday); Place: S16-03-07 4 questions The focus is primarily on the modeling of derivative pricing Consultation time: 4:30pm-6:30pm on 23 Nov, and 2:30pm-4:30pm 24 Nov, or any time by appointment.