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Author Musiela, Marek, 1950-

Title Martingale methods in financial modelling / Marek Musiela, Marek Rutkowski
Published Berlin ; New York : Springer, [1997]


Location Call no. Vol. Availability
Description xii, 512 pages ; 24 cm
regular print
Series Applications of mathematics, 0172-4568 ; 36
Applications of mathematics. 0172-4568 ; 36
Contents 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 -- 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 -- App. A. Conditional Expectations -- App. B. Ito Stochastic Calculus
Summary The book provides a comprehensive, self-contained and up-to-date treatment of the main topics in the theory of option pricing. The first part of the text deals with simple discrete models of financial markets, including the Cox-Ross-Rubinstein binomial model. No knowledge of probability and stochastic processes is assumed at this stage, while most of the concepts from modern mathematical finance are explained at a very elementary mathematical level. The passage from the discrete to the continuous market models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus such as Wiener process and Ito formula; however, an appendix containing all the necessary results is included. The Black-Scholes setting is later generalized to cover standard and exotic options involving several assets and/or currencies. Numerous examples of exotic options are analysed. An outline of a general theory of arbitrage pricing is presented. A very substantial part of the text is devoted to term structure modelling and to the pricing of interest rate options. The HJM framework is discussed in detail. Models based on the forward LIBOR and forward swap rates are introduced. The main emphasis is on models that can be made consistent with the market pricing practice
Analysis finans√łkonomi
Bibliography Includes bibliographical references (pages [471]-506) and index
Subject Derivative securities -- Mathematical models.
Finance -- Mathematical models.
Fixed-income securities -- Mathematical models.
Interest rates -- Mathematical models.
Options (Finance) -- Mathematical models.
Author Rutkowski, Marek, 1952-
LC no. 97011586
ISBN 354061477X