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A general control variate method for time-changed Lévy processes: An application to option pricing

Kenichiro Shiraya, Cong Wang and Akira Yamazaki
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Kenichiro Shiraya: Graduate School of Economics, The University of Tokyo
Cong Wang: Graduate School of Economics, The University of Tokyo
Akira Yamazaki: Graduate School of Business Administration, Hosei University

No CARF-F-499, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

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 our method, we generate a highly-correlated process with an underlying price process generated by the time-changed Lévy model. We then apply the characteristic function approach with the 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.

Pages: 26
Date: 2020-12, Revised 2021-01
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