Calibration of multivariate stochstic volatility models

Jörg Kampen

Abstract: We consider multivariate continuous semimartingale models for asset dynamics with stochastic volatility driven by a vector-valued Lévy process which can be correlated with the Brownian motion. Assuming that the background driving process is ergotic we provide estimators of the effective volatility matrix on the basis of high frequency data. Under some scaling assumptions on the martingale parts of the background driving processes asymptotic formulas for the option prices are derived extending results of Papanicolaou et al. to a more general situation. We present fast converging recursion formulas for the correction constants occuring in the asymptotic option price formulas which allow for computing the correction constants for high dimensional models on the basis of the high frequency returns. We indicate that our methods of estimating the effective volatility matrix can be used to get estimators for the spot volatilities. This allows for asymptotic calibration on a shorter time scale. The results are underlined by simulations for bivariate stochastic volatility models with classicla mean-reversion Orstein-Uhlenbeck background driving processes.

The presentation is based on a joint work with N. Surulescu.

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