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**Mathematical models of financial derivatives.
2nd ed.**
*(English)*
Zbl 1146.91002

Springer Finance. Berlin: Springer (ISBN 978-3-540-42288-4/hbk). xv, 530 p. (2008).

This book is written mainly as a textbook of modelling on derivative pricing theory for the students in financial engineering, computational finance etc. It provides basic knowledge of mathematical theory and applications of the financial derivatives. Basically based on the Black-Scholes model or the Black-Scholes model extended with some simple jumps of the underlying equities, in the present book, wide derivatives, including options and their compounding, futures, swaps, exploited respectively in European type, Asian type, American type, and Russian type are analyzed, of most of which the pricing methods are formulated in sophisticated mathematical closed form which would fit the application of those people in economy and business, as well as for those in mathematics and MBA. Compared to the classical textbook <Options, futures and other derivatives> written by John Hull, the present book gives more mathematical analysis and formulation. Besides, variants of financial products are also recommended. To understand this book, prerequisite knowledge of calculus, probability and statistics are necessary. A close look at its eight chapters may be helpful to understand this book :

Chapter 1 - Introduction to derivative instrument. It offers the general concepts of the derivatives, including rational boundary for option values, swaps. Chapter 2 - Financial economics and stochastic calculus. this chapter focuses the discrete models and the elementary concepts of the stochastic calculus. Chapter 3 - Option pricing models : Black-Scholes formulation. Except the classical model, extended option models and Black-Scholes model with jumps, stochastic volatility models are also discussed. Chapter 4 - Path denpendent options. Barrier options, lookback options and Asian option are considered. Chapter 5 - American options. Approximation methods and options with voluntary reset right are explained. Chapter 6 -Numerical schemes for pricing options. Lattice tree methods, finite difference algorithms and Monte Carlo simulations are presented. Chapter 7 - Interest rates models and bond pricing. Multifactor interest rate models and HJM framework are observed. Chapter 8 - Interest derivatives: Bond options, LIBOR and swap products. This book can also be used as an Instructor’s Manual of reference of those in financial institutions.

Chapter 1 - Introduction to derivative instrument. It offers the general concepts of the derivatives, including rational boundary for option values, swaps. Chapter 2 - Financial economics and stochastic calculus. this chapter focuses the discrete models and the elementary concepts of the stochastic calculus. Chapter 3 - Option pricing models : Black-Scholes formulation. Except the classical model, extended option models and Black-Scholes model with jumps, stochastic volatility models are also discussed. Chapter 4 - Path denpendent options. Barrier options, lookback options and Asian option are considered. Chapter 5 - American options. Approximation methods and options with voluntary reset right are explained. Chapter 6 -Numerical schemes for pricing options. Lattice tree methods, finite difference algorithms and Monte Carlo simulations are presented. Chapter 7 - Interest rates models and bond pricing. Multifactor interest rate models and HJM framework are observed. Chapter 8 - Interest derivatives: Bond options, LIBOR and swap products. This book can also be used as an Instructor’s Manual of reference of those in financial institutions.

Reviewer: Gong Guanglu (Beijing)

### MSC:

91-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to game theory, economics, and finance |

91G20 | Derivative securities (option pricing, hedging, etc.) |