Introduction to stochastic calculus applied to finance

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Chapman & Hall/CRC, 2008 - Business & Economics - 253 pages
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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 numéraire 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.

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Contents

Introduction
9
Discretetime models
15
Optimal stopping problem and American options
37
Brownian motion and stochastic differential equations
51
The BlackScholes model
87
Option pricing and partial differential equations
123
Interest rate models
149
Asset models with jumps
173
Credit risk models
195
Simulation and algorithms for financial models
207
Appendix
235
Bibliography
243
Index
251
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