Financial Modelling with Jump Processes
CRC Press, 30 déc. 2003 - 552 pages
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.
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Part I Mathematical tools
Part II Simulation and estimation
Part III Option pricing in models with jumps
Part IV Beyond Lévy processes
additive process algorithm approximation arbitrage asset barrier options behavior Brownian motion cadlag calibration call option Chapter characteristic function characteristic triplet component compound Poisson process compute condition continuous convergence corresponding defined definition denoted diffusion models discussed drift equation estimation European option example exponent exponential exponential-Lévy models finite variation Fourier transform gamma process given implied volatility infinitely divisible intensity Itô formula jump processes jump sizes jump-diffusion model Lévy density Lévy measure Lévy process Markov maturity methods minimal models with jumps Monte Carlo nonanticipating obtain option prices parameters payoff PIDE Poisson random measure portfolio predictable processes pricing rule probability measure problem proof properties Proposition random variable relative entropy result returns risk risk-neutral sample paths Section self-similarity semimartingale series representation simulate skew small jumps stochastic integral stochastic process stochastic volatility stochastic volatility models subordinator tail integrals tempered stable process theorem trajectory variance gamma verifies Wiener process zero