A balanced introduction to the theoretical foundations and real-world applications of mathematical financeThe ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models.Utilizing almost twenty years of academic and industry experience, the author discusses the mathematical concepts that are the foundation of commonly used derivative pricing models, and insightful Motivation and Interpretation sections for each concept are presented to further illustrate the relationship between theory and practice. In-depth coverage of the common characteristics found amongst successful pricing models are provided in addition to key techniques and tips for the construction of these models. The opportunity to interactively explore the book's principal ideas and methodologies is made possible via a related Web site that features interactive Java experiments and exercises.While a high standard of mathematical precision is retained, Mathematical Finance emphasizes practical motivations, interpretations, and results and is an excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level. It also serves as a valuable reference for professionals in the banking, insurance, and asset management industries.

1. Introduction.I: FOUNDATIONS.2. Foundations.3. Replication.II: FIRST APPLICATIONS.4. Pricing of a European Stock Option under the Black-Scholes Model.5. Excursus: The Density of the Underlying of a European Call Option.6. Excursus: Interpolation of European Option Prices.7. Hedging in Continuous and Discrete Time and the Greeks.III: INTEREST RATE STRUCTURES, INTEREST RATE PRODUCTS AND ANALYTIC PRICING FORMULAS.Motivation and Overview.8. Interest Rate Structures.9. Simple Interest Rate Products.10. The Black Model for a Caplet.11. Pricing of a Quanto Caplet (Modeling the FFX).12. Exotic Derivatives.IV: DISCRETIZATION AND NUMERICAL VALUATION METHODS.Motivation and Overview.13. Discretization of time and state space.14. Numerical Methods for Partial Differential Equations.15. Pricing Bermudan Options in a Monte Carlo Simulation.Method.16. Pricing Path-Dependent Options in a Backward Algorithm.17. Sensitivities (Partial Derivatives) of Monte Carlo Prices.18. Proxy Simulation Schemes for Monte Carlo Sensitivities and Importance Sampling.V: PRICING MODELS FOR INTEREST RATE DERIVATIVES.19. LIBOR Market Models.20. Swap Rate Market Models.21. Excursus: Instantaneous Correlation and Terminal Correlation.22.Heath-Jarrow-Morton Framework: Foundations.23. Short-Rate Models.24 Heath-Jarrow-Morton Framwork: Immersion of Short-Rate Models and LIBOR Market Model.25. Excursus: Shape of teh Interst Rate Curve under Mean Reversion and a Multifactor Model.26. Ritchken-Sakarasubramanian Framework: JHM with Low Markov Dimension.Markov Functional Models.PART VI: Extended Models.28. Credit Spreads.29. Hybrid Models.PART VII: Implementation30. Object-Oriented Implementatin in Java(TM).PART VIII: Appendices.A: A small Collection of Common Misconceptions.B: Tools (Selection).C: Exercises.D: List of Symbols.E: Java(TM) Source Code (Selection).List of Figures.List of Tables.List of Listings.Bibliography.Index.