Financial Modelling with Jump Processes

Rama Cont, Peter Tankov - Collection Financial Mathematics Series

535 pages, parution le 04/02/2004

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Résumé

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 does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by its 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.

Presents the concepts and tools for using jump processes in modeling market fluctuations
Uses clear exposition and intuitive explanations to demystify the technicalities and make the tools accessible to nonspecialists
Clarifies mathematical concepts with empirical and numerical examples and almost 200 figures and tables
Details the numerical implementation of pricing and calibration algorithms
Provides additional materials and new development on a supporting Web site

L'auteur - Rama Cont

Ecole Polytechnique, France

L'auteur - Peter Tankov

Ecole Polytechnique, France

Sommaire

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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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Rama Cont, Peter Tankov
Collection	Financial Mathematics Series
Parution	04/02/2004
Nb. de pages	535
Format	16 x 24
Couverture	Relié
Poids	890g
Intérieur	Noir et Blanc
EAN13	9781584884132
ISBN13	978-1-5848-8413-2