Symmetrization associated with hyperbolic reflection principle

Abstract

Abstract In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura’s symmetrization. Some results of numerical experiments, which imply the efficiency of the numerical scheme based on the symmetrization, are given.

Keywords

• Hyperbolic Brownian motion
• Reflection principle
• Symmetrization
• Barrier option
• Euler-Maruyama scheme