Ebook: Martingale Methods in Financial Modelling

This 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 starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.

In the 2^nd edition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk.

In the 3^rd printing of the 2^nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail.

As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.

Part II of the book has been revised fundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is available. The authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions. In particular, it should concentrate on defining liquid primary and derivative assets and identifying the relevant sources of trading risk.

This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on the practical rather than the theoretical aspects of financial modelling.

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This 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 starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.

In the 2^nd edition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk.

In the 3^rd printing of the 2^nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail.

As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.

Part II of the book has been revised fundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is available. The authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions. In particular, it should concentrate on defining liquid primary and derivative assets and identifying the relevant sources of trading risk.

This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on the practical rather than the theoretical aspects of financial modelling.

---

This 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 starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.

In the 2^nd edition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk.

In the 3^rd printing of the 2^nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail.

As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.

Part II of the book has been revised fundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is available. The authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions. In particular, it should concentrate on defining liquid primary and derivative assets and identifying the relevant sources of trading risk.

This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on the practical rather than the theoretical aspects of financial modelling.

Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
An Introduction to Financial Derivatives....Pages 3-34
Discrete-time Security Markets....Pages 35-111
Benchmark Models in Continuous Time....Pages 113-179
Foreign Market Derivatives....Pages 181-204
American Options....Pages 205-228
Exotic Options....Pages 229-252
Volatility Risk....Pages 253-314
Continuous-time Security Markets....Pages 315-347
Front Matter....Pages 349-349
Interest Rates and Related Contracts....Pages 351-381
Short-Term Rate Models....Pages 383-416
Models of Instantaneous Forward Rates....Pages 417-467
Market LIBOR Models....Pages 469-516
Alternative Market Models....Pages 517-571
Cross-currency Derivatives....Pages 573-607
Back Matter....Pages 609-715

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This 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 starts with discrete-time models of financial markets, including the Cox-Ross-Rubinstein binomial model. The passage from discrete- to continuous-time models, done in the Black-Scholes model setting, assumes familiarity with basic ideas and results from stochastic calculus. However, an Appendix containing all the necessary results is included. This model setting is later generalized to cover standard and exotic options involving several assets and/or currencies. An outline of the general theory of arbitrage pricing is presented. The second part of the text is devoted to the term structure modelling and the pricing of interest-rate derivatives. The main emphasis is on models that can be made consistent with market pricing practice.

In the 2^nd edition, some sections of the former Part I are omitted for better readability, and a brand new chapter is devoted to volatility risk.

In the 3^rd printing of the 2^nd edition, the second Chapter on discrete-time markets has been extensively revised. Proofs of several results are simplified and completely new sections on optimal stopping problems and Dynkin games are added. Applications to the valuation and hedging of American-style and game options are presented in some detail.

As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.

Part II of the book has been revised fundamentally. The theme of volatility risk appears systematically. Much more detailed analysis of the various interest-rate models is available. The authors' perspective throughout is that the choice of a model should be based on the reality of how a particular sector of the financial market functions. In particular, it should concentrate on defining liquid primary and derivative assets and identifying the relevant sources of trading risk.

This long-awaited new edition of an outstandingly successful, well-established book, concentrating on the most pertinent and widely accepted modelling approaches, provides the reader with a text focused on the practical rather than the theoretical aspects of financial modelling.

Content:
Front Matter....Pages i-xix
Front Matter....Pages 1-1
An Introduction to Financial Derivatives....Pages 3-34
Discrete-time Security Markets....Pages 35-111
Benchmark Models in Continuous Time....Pages 113-179
Foreign Market Derivatives....Pages 181-204
American Options....Pages 205-228
Exotic Options....Pages 229-252
Volatility Risk....Pages 253-314
Continuous-time Security Markets....Pages 315-347
Front Matter....Pages 349-349
Interest Rates and Related Contracts....Pages 351-381
Short-Term Rate Models....Pages 383-416
Models of Instantaneous Forward Rates....Pages 417-467
Market LIBOR Models....Pages 469-516
Alternative Market Models....Pages 517-571
Cross-currency Derivatives....Pages 573-607
Back Matter....Pages 609-715
....