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Malliavin-Skorohod Calculus for Additive Processes with Applications to Finance Chapman & Hall/CRC Monographs and Research Notes in Mathematics Series

Langue : Anglais

Auteur :

The purpose of the book is to present the Malliavin-Skorohod calculus for additive processes, that is, processes with independent increments; in other words, Lévy processes without the hypothesis of stationarity of increments. This will be the addition of Malliavin calculus for Gaussian processes and Malliavin calculus for Poisson random measures. The second is the application of the previous theory to finance, concretely, to stochastic volatility jump diffusion models, in order to solve problems related with pricing and hedging via Clark-Ocone formula, computation of sensitivities, obtaining useful price decompositions (Hull and White type formulas) and local risk minimizing strategies.

Introduction: Lévy and Additive Processes, Lévy Processes in Finance. Malliavin-Skorohod Type Calculus without Probabilities: The Fock Space Setting. Additive Processes: The Chaotic Representation Propert. Malliavin-Skorohod Calculus for Gaussian Processes: A Review. Malliavin-Skorohod Calculus for Poisson Random Measures in the Canonical Space. Examples: The Cases of Standard Poisson Process and Simple Lévy Process. Clark-Hausmann-Ocone Formula. Pricing and Hedging Financial Derivatives. Sensitivity Analysis for Stochastic Volatility Additive Models. Price Decomposition for Stochastic Volatility Jump Diffusion Models and Applications. Local Risk Minimizing Hedging Strategies.

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