Financial Modelling with Jump Processes

Financial Modelling with Jump Processes

3.14 (7 ratings by Goodreads)
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WINNER of a 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 Levy 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, Levy 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.
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Product details

  • Hardback | 552 pages
  • 156 x 244 x 34mm | 898.13g
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 1000 equations; 20 Tables, black and white; 53 Illustrations, black and white
  • 1584884134
  • 9781584884132
  • 829,812

Table of contents

Models in the light of empirical facts
Evidence from option markets
Implied volatility smiles and skews
Short term options
Hedging and risk management

Basic Tools
Levy Processes: Definitions and Properties
Building Levy processes
Multidimensional Models with Jumps

Simulating Levy Processes
Modelling Financial Time Series with Levy Processes

Stochastic Calculus for Jump Processes
Measure Transformations for Levy Processes
Pricing and Hedging in Incomplete Markets
Risk-Neutral Modelling with Exponential Levy Processes
Integro-Differential Equations and Numerical Methods
Inverse Problems and Model Calibration

Time-Inhomogeneous Models
Stochastic Volatility Models with Jumps

APPENDIX: Modfied Bessel Functions
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Review quote

"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 for recent developments in the use of jump processes in financial modelling, in particular the use of lKvy 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 in the '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 of '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
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Rating details

7 ratings
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3 29% (2)
2 14% (1)
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