A General Control Variate Method for LÃ©vy Models in Finance
Hiroki Uenishi and
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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
This study proposes a new control variate method for LÃ©vy models in finance.Our method generates a process of the control variate whose initial and terminal values coincide with those of the target LÃ©vy 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.
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