Numerical Method for KoBol Fractional Option Pricing Model

Abstract:

Since the Black-Scholes model was proposed， many option pricing models have been proposed， which has become a hotspot in financial engineering. For the past few years， option pricing models based on Lévy process such as FMLS， CGMY and KoBol have drawn great attention because of their capability to represent the dynamic characteristics of underlying asset. Solving these models would eventually come down to solving a class of fractional partial differential equations. In this paper， a numerical scheme is proposed for the class of FPDE and the stable condition of the scheme is given. The numerical experiments prove the feasibility and effectiveness of the proposed numerical scheme. Based on the practical data of SSE 50ETF and CSI 300ETF index option， the option price and volatility curve are calculated to verify the effectiveness of KoBol model in real market.