A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.

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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.