Introduction to Stochastic Calculus Applied to Finance / Edition 1

Introduction to Stochastic Calculus Applied to Finance / Edition 1

by Damien Lamberton
     
 

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… See more details below

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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Product Details

ISBN-13:
9780412718007
Publisher:
Springer-Verlag New York, LLC
Publication date:
06/01/1996
Edition description:
Older Edition
Pages:
200
Product dimensions:
6.10(w) x 9.70(h) x 0.60(d)

Table of Contents

Introduction
1Discrete-time models1
2Optimal stopping problem and American options17
3Brownian motion and stochastic differential equations29
4The Black-Scholes model63
5Option pricing and partial differential equations95
6Interest rate models121
7Asset models with jumps141
8Simulation and algorithms for financial models161
App. A.1 Normal random variables173
App. A.2 Conditional expectation174
App. A.3 Separation of convex sets178
References179
Index183

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