Introduction to Stochastic Calculus Applied to Finance

ISBN-13: 9781584886266 / Angielski / Twarda / 2007 / 254 str.

Damien Lamberton; Lamberton Lamberton; Bernard Lapeyre

Opis

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.

Recenzje

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

Spis treści

INTRODUCTION DISCRETE-TIME MODELS Discrete-time formalismMartingales 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 processesBrownian 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 martingalesPricing and hedging options in the Black-Scholes model American options Implied volatility and local volatility modelsThe Black-Scholes model with dividends and call/put symmetry ProblemsOPTION PRICING AND PARTIAL DIFFERENTIAL EQUATIONS European option pricing and diffusions Solving parabolic equations numerically American options INTEREST RATE MODELS Modeling principlesSome classical modelsASSET MODELS WITH JUMPS Poisson processDynamics 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 CopulasSIMULATION AND ALGORITHMS FOR FINANCIAL MODELS Simulation and financial models Introduction to variance reduction methods Computer experimentsAPPENDIX Normal random variablesConditional expectationSeparation of convex sets BIBLIOGRAPHYINDEXExercises appear at the end of each chapter.

O autorze

Damien Lamberton, Bernard Lapeyre