Introduction to Stochastic Calculus Applied to Finance
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Introduction to Stochastic Calculus Applied to Finance

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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 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.show more

Product details

  • Hardback | 254 pages
  • 154.94 x 236.22 x 20.32mm | 476.27g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • black & white illustrations
  • 1584886269
  • 9781584886266
  • 595,224

Review quote

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. 2show more

Table of contents

INTRODUCTION DISCRETE-TIME MODELS Discrete-time formalism Martingales and arbitrage opportunities Complete markets and option pricing Problem: Cox, Ross and Rubinstein model OPTIMAL STOPPING PROBLEM AND AMERICAN OPTIONS Stopping time The Snell envelope Decomposition of supermartingales Snell envelope and Markov chains Application to American options BROWNIAN MOTION AND STOCHASTIC DIFFERENTIAL EQUATIONS General comments on continuous-time processes Brownian motion Continuous-time martingales Stochastic integral and Ito calculus Stochastic differential equations THE BLACK-SCHOLES MODEL Description of the model Change of probability: Representation of martingales Pricing and hedging options in the Black-Scholes model American options Implied volatility and local volatility models The Black-Scholes model with dividends and call/put symmetry Problems OPTION PRICING AND PARTIAL DIFFERENTIAL EQUATIONS European option pricing and diffusions Solving parabolic equations numerically American options INTEREST RATE MODELS Modeling principles Some classical models ASSET MODELS WITH JUMPS Poisson process Dynamics of the risky asset Martingales in a jump-diffusion model Pricing options in a jump-diffusion model CREDIT RISK MODELS Structural models Intensity-based models Copulas SIMULATION AND ALGORITHMS FOR FINANCIAL MODELS Simulation and financial models Introduction to variance reduction methods Computer experiments APPENDIX Normal random variables Conditional expectation Separation of convex sets BIBLIOGRAPHY INDEX Exercises appear at the end of each chapter.show more

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