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A General Control Variate Method for Lévy Models in Finance

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

No CARF-F-455, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: This study proposes a new control variate method for Lévy models in finance.Our method generates a process of the control variate whose initial and terminal values coincide with those of the target Lévy model process, with both processes being driven by the same Brownian motion in the simulation. These features efficiently reduce the variance of the Monte Carlo simulation. As a typical application of this method, we provide the calculation scheme for pricing path-dependent exotic options. We use numerical experiments to examine the validity of our method for both continuously and discretely monitored path-dependent options under variance gamma and normal inverse Gaussian models.

New Economics Papers: this item is included in nep-cmp
Date: 2019-10
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