A Second Order Numerical Scheme for Fractional Option Pricing Models

Abstract

A number of fractional option models (FMLS, CGMY, KoBol) are proposed and studied under assumption that the motion of the underlying assets follows a Lévy process. Numerical methods for these option pricing models are based on solution of fractional partial differential equations. To discretise them, we employ a second order numerical scheme and study its stability and convergence. Numerical experiments show the efficiency of the method and its convergence. Simulations related to practical stock markets, further confirm the robustness of the scheme and show that KoBol model has advantage over the classical Black-Scholes model.