Introduction to Stochastic Calculus Applied to Finance, Second Edition (Chapman & Hall/Crc Financial Mathematics Series)

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. Read more... Abstract: Suitable for students of mathematical finance, or a quick introduction to researchers and finance practitioners. This book covers the stochastic calculus theory required, as well as many key finance topics, including a chapter dedicated to credit risk modeling. Read more...

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.

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, this concise and accessible introduction covers the probabilistic techniques required to understand the most widely used financial models. Along with additional exercises, this edition presents fully updated material on stochastic volatility models and option pricing as well as a new chapter on credit risk modeling. It contains many numerical experiments and real-world examples taken from the authors' own experiences. The book also provides all of the necessary stochastic calculus theory and implements some of the algorithms using SciLab. Key topics covered include martingales, arbitrage, option pricing, and the Black-Scholes model. Front cover 1 Preface to the second edition 7 Contents 9 Introduction 11 Chapter 1: Discrete-time models 17 Chapter 2: Optimal stopping problem and American options 39 Chapter 3: Brownian motion and stochastic dierentialequations 53 Chapter 4: The Black-Scholes model 89 Chapter 5: Option pricing and partial differential equations 125 Chapter 6: Interest rate models 151 Chapter 7: Asset models with jumps 175 Chapter 8: Credit risk models 197 Chapter 9: Simulation and algorithms for financial models 209 Appendix 237 Bibliography 245 Back cover 253 "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 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."--Jacket Content: Front cover Preface to the second edition Contents Introduction Chapter 1: Discrete-time models Chapter 2: Optimal stopping problem and American options Chapter 3: Brownian motion and stochastic di ̇erentialequations Chapter 4: The Black-Scholes model Chapter 5: Option pricing and partial differential equations Chapter 6: Interest rate models Chapter 7: Asset models with jumps Chapter 8: Credit risk models Chapter 9: Simulation and algorithms for financial models Appendix Bibliography Back cover Maintaining the concise style of its predecessor, this book is a new edition of a very popular text in mathematical finance. This edition has been fully updated, with many sections greatly enhanced, and new material incorporated on stochastic volatility models, options pricing and credit risk modelling The objective of this chapter is to present the main ideas related to option theory within the very simple mathematical framework of discrete-time models.