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Introduction to Stochastic Calculus Applied to Finance / Edition 1

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Overview

Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor, Introduction to Stochastic Calculus Applied to Finance, Second Edition incorporates some of these new techniques and concepts to provide an accessible, up-to-date initiation to the field.

New to the Second Edition: Complements on discrete models, including Rogers' approach to the fundamental theorem of asset pricing and super-replication in incomplete markets, Discussions on local volatility, Dupire's formula, the change of numeraire techniques, forward measures, and the forward Libor model, A new chapter on credit risk modeling, An extension of the chapter on simulation with numerical experiments that illustrate variance reduction techniques and hedging strategies, Additional exercises and problems.

Providing all of the necessary stochastic calculus theory, the authors cover many key finance topics, including martingales, arbitrage, option pricing, American and European options, the Black-Scholes model, optimal hedging, and the computer simulation of financial models. They succeed in producing a solid introduction to stochastic approaches used in the financial world. Features: Provides a concise and accessible introduction to the probabilistic techniques required to understand the most widely used financial models, Presents fully updated material on stochastic volatility models, option pricing, and credit risk modeling, Includes many numericalexperiments and real-world examples taken from the authors' own experiences, Implements some algorithms using SciLab.

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Editorial Reviews

From the Publisher
The second edition of this book provides a concise and accessible introduction to the probabilistic techniques needed to understand the most widely used financial models. This edition incorporates many new techniques and concepts to be used to describe the behavior of financial markets. … the solutions obtained using SciLab for computer experiments are available at http://cermics.enpc.fr/~bl/scilab/ These experiments were well designed by the authors based on their teaching and research experience and were found to be effective in communicating these concepts and ideas and enhancing the understanding of readers. … a solid introduction to stochastic approaches used in the financial world. The authors cover many key finance topics … . The book can be used as a reference text by researchers and graduate students in financial mathematics. It also is ideal reading material for practicing financial analysts and consultants using mathematical models for finance.
Technometrics, May 2009, Vol. 51, No. 2
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Product Details

  • ISBN-13: 9780412718007
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 6/1/1996
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 200
  • Product dimensions: 6.10 (w) x 9.70 (h) x 0.60 (d)

Table of Contents

Introduction
1 Discrete-time models 1
2 Optimal stopping problem and American options 17
3 Brownian motion and stochastic differential equations 29
4 The Black-Scholes model 63
5 Option pricing and partial differential equations 95
6 Interest rate models 121
7 Asset models with jumps 141
8 Simulation and algorithms for financial models 161
App. A.1 Normal random variables 173
App. A.2 Conditional expectation 174
App. A.3 Separation of convex sets 178
References 179
Index 183
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