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Financial Modelling with Jump Processes




ISBN 9781584884132
Published December 30, 2003 by Chapman and Hall/CRC
552 Pages - 53 B/W Illustrations

 
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Book Description

WINNER of a Riskbook.com Best of 2004 Book Award!

During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Lévy processes are beyond their reach.

Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by their use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations.

Topics covered in this book include: jump-diffusion models, Lévy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms.

This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.

Table of Contents

FINANCIAL MODELLING BEYOND BROWNIAN MOTION 1
Models in the light of empirical facts
Evidence from option markets
Implied volatility smiles and skews
Short term options
Hedging and risk management
Objectives

MATHEMATICAL TOOLS
Basic Tools
Lévy Processes: Definitions and Properties
Building Lévy processes
Multidimensional Models with Jumps

SIMULATION AND ESTIMATION
Simulating Lévy Processes
Modelling Financial Time Series with Lévy Processes

OPTION PRICING IN MODELS WITH JUMPS
Stochastic Calculus for Jump Processes
Measure Transformations for Lévy Processes
Pricing and Hedging in Incomplete Markets
Risk-Neutral Modelling with Exponential Lévy Processes
Integro-Differential Equations and Numerical Methods
Inverse Problems and Model Calibration

BEYOND LÉVY PROCESSES
Time-Inhomogeneous Models
Stochastic Volatility Models with Jumps

APPENDIX: Modfied Bessel Functions
REFERENCES
SUBJECT INDEX

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Reviews

"Pardon the pun, but I jumped at the opportunity to endorse this book. This book is the first complete treatment of markets rendered incomplete by the reality of jumps in prices and volatilities. If I were you, I would pounce."
-Dr. Peter Carr, Head of Quantitative Research, Bloomberg LP and Director of Masters Program in Mathematical Finance, NYU

"This book is an extremely rich source of information…the content speaks for itself…"
-ISI Short Book Reviews

"This book is an extremely rich source of information for recent developments in the use of jump processes in financial modelling, in particular the use of Levy processes. The authors work at a comfortable mathematical pace choosing carefully which proofs to include and exclude and never losing sight of financial interpretation and application.

"The authors conclude the main body of their text by saying: 'We hope that the present volume will encourage more researchers and practitioners to contribute to this topic and improve on our understanding of theoretical, numerical and practical issues related to financial modelling with jump processes'. I am quite convinced that this goal will be achieved."
-Dr. Andreas E. Kyprianou, International Statistics Institute book reviews

"What makes this book attractive is its comprehensiveness. … this is an excellent book. Read it. You will learn much."
-Glyn A. Holton, Contingency Analysis

"One of the first texts which is entirely devoted to option pricing with non-continuous jump-type stochastic processes … an easygoing presentation where the basic problems of jump models are not additionally obscured by technicalities."
-Journal of the Royal Statistics

"I love this book. It will be required reading for students entering Levy finance. My judgment is that it will be useful both within academia, particularly to people in stochastics, econometrics, and other fields wanting to develop an interest in finance, and to practitioners."
-N.H. Bingham, Journal of the American Statistical Association