Martingale Methods in Financial Modelling / Edition 2

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Overview

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.
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Product Details

  • ISBN-13: 9783540209669
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 4/28/2011
  • Series: Stochastic Modelling and Applied Probability Series , #36
  • Edition description: 2nd ed. 2005. Corr. 3rd printing 2009
  • Edition number: 2
  • Pages: 654
  • Product dimensions: 6.40 (w) x 9.50 (h) x 1.70 (d)

Table of Contents

Preface
1 An Introduction to Financial Derivatives 3
2 The Cox-Ross-Rubinstein Model 33
3 Finite Security Markets 69
4 Market Imperfections 87
5 The Black-Scholes Model 109
6 Modifications of the Black-Scholes Model 135
7 Foreign Market Derivatives 159
8 American Options 183
9 Exotic Options 205
10 Continuous-time Security Markets 229
11 Interest Rates and Related Contracts 265
12 Models of the Short-term Rate 281
13 Models of Instantaneous Forward Rates 303
14 Models of Bond Prices and LIBOR Rates 325
15 Option Valuation in Gaussian Models 357
16 Swap Derivatives 387
17 Cross-currency Derivatives 419
App. A Conditional Expectations 455
App. B Ito Stochastic Calculus 459
References 471
Index 507
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