Martingale Methods in Financial Modelling

I. Spot and Futures Markets.- 1. An Introduction to Financial Derivatives.- 2. The Cox-Ross-Rubinstein Model.- 3. Finite Security Markets.- 4. Market Imperfections.- 5. The Black-Scholes Model.- 6. Modifications of the Black-Scholes Model.- 7. Foreign Market Derivatives.- 8. American Options.- 9. Exotic Options.- 10. Continuous-time Security Markets.- II. Fixed-income Markets.- 11. Interest Rates and Related Contracts.- 12. Models of the Short-term Rate.- 13. Models of Instantaneous Forward Rates.- 14. Models of Bond Prices and LIBOR Rates.- 15. Option Valuation in Gaussian Models.- 16. Swap Derivatives.- 17. Cross-currency Derivatives.- III. Appendices.- A. Conditional Expectations.- B. Itô Stochastic Calculus.- References.