A general control variate method for time-changed Lévy processes: an application to options pricing

Kenichiro Shiraya; Cong Wang; Akira Yamazaki

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We propose a new and efficient control variate method combined for pricing path-dependent options under time-changed Lévy models.
We construct a highly correlated process as a control variate whose characteristic function is obtained by using the fast Fourier transform.
Our method can be applied to a wide range of options and is more versatile than other past methods.
The variance of Monte Carlo is reduced efficiently in our numerical experiments.

Abstract

We propose a new control variate method combined with a characteristic function approach for pricing path-dependent options under time-changed Lévy models. In this method, we generate a process that is highly correlated with an underlying price process generated by the time-changed Lévy model. We then apply the characteristic function approach with a fast Fourier transform to obtain the expected payoff of the corresponding option under the correlated process. In numerical experiments, we employ three types of path-dependent options and six types of time-changed Lévy models to confirm the efficiency of our method. To the best of our knowledge, this paper is the first to develop an efficient control variate method for time-changed Lévy models.

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