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A new technique for calibrating stochastic volatility models: the Malliavin gradient method |
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| Authors: | Christian-Oliver Ewald Aihua Zhang |
| Institution: | 1. School of Mathematics , University of Leeds , Leeds LS2 9JT, UK ewald@leeds.ac.uk;3. Fraunhofer Institute ITWM , University of Kaiserslautern , Kaiserslautern, 67663, Germany |
| Abstract: | We discuss the application of gradient methods to calibrate mean reverting stochastic volatility models. For this we use formulas based on Girsanov transformations as well as a modification of the Bismut–Elworthy formula to compute the derivatives of certain option prices with respect to the parameters of the model by applying Monte Carlo methods. The article presents an extension of the ideas to apply Malliavin calculus methods in the computation of Greek's. |
| Keywords: | Malliavin calculus Monte Carlo simulation Stochastic volatility models Calibration Gradient methods Value at risk |