ISBN: 1584884134,
ISBN13: 9781584884132,
552 pages, hardback, published by Chapman & Hall, illustrated edition edition, 2004
Description of Financial Modelling with Jump Processes
This title is 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 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, and 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.
Contents of Financial Modelling with Jump Processes
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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