Introduction to Stochastic Calculus Applied to Finance: 2nd Edition (Hardback) book cover

Introduction to Stochastic Calculus Applied to Finance

2nd Edition

By Damien Lamberton, Bernard Lapeyre

Chapman and Hall/CRC

254 pages

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Hardback: 9781584886266
pub: 2007-11-30
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pub: 2011-12-14
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Description

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.

  • Reviews

    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

    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 Itô 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.

    About the Series

    Chapman and Hall/CRC Financial Mathematics Series

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    BUS027000
    BUSINESS & ECONOMICS / Finance
    MAT000000
    MATHEMATICS / General
    MAT029000
    MATHEMATICS / Probability & Statistics / General