Hyperbolic Symmetrization of Heston Type Diffusion
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The symmetrization of diffusion processes was originally introduced by Imamura, Ishigaki and Okumura, and was applied to pricing of barrier options. The authors of the present paper previously introduced in Ida et al. (Pac J Math Ind 10:1, 2018) a hyperbolic version of the symmetrization of a diffusion by symmetrizing drift coefficient in view of applications under a SABR model which is transformed to a hyperbolic Brownian motion with drift. In the present paper, in order to apply the hyperbolic symmetrization technique to Heston model, we introduce an extension where diffusion coefficient is also symmetrized. Some numerical results are also presented.
KeywordsHeston model Symmetrization Euler–Maruyama scheme Hyperbolic space Numerical simulation
The authors deeply thank Prof. Jirô Akahori for his warm support.