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Published in:
2009 | OriginalPaper | Chapter
The Weighted Variance Minimization in Jump-Diffusion Stochastic Volatility Models
Authors : Anatoly Gormin, Yuri Kashtanov
Published in: Monte Carlo and Quasi-Monte Carlo Methods 2008
Publisher: Springer Berlin Heidelberg
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The Monte Carlo method is applied to estimation of options in the case of a stochastic volatility model with jumps. An option contract has a number of parameters like a strike, an exercise date, etc. Estimators of option prices with different values of its parameters are constructed on the same trajectories of the underlying asset price process. The problem of minimization of the weighted sum of their variances is considered. Optimal estimators with minimal weighted variance are pointed out. Their approximations are applied to variance reduction.