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Financial Modelling with Jump Processes
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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
Levy Processes: Definitions and Properties
Building Levy processes
Multidimensional Models with Jumps

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

OPTION PRICING IN MODELS WITH JUMPS
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

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

APPENDIX: Modfied Bessel Functions
REFERENCES
SUBJECT INDEX

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 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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