Time fractional CGMY model for the numerical pricing of European call options

Abstract

Evolutionary equations containing fractional derivatives have been widely used in financial models and can describe anomalous diffusion and transmission dynamics in some complex systems. We assumes that option pricing obeys the infinite jump CGMY process and treats stock price fluctuations as a fractal transmission system, A time fractional CGMY option pricing (TFCGMY) model is obtained. The L1 approximation of the Caputo fractional derivative and the modified GL approximation are used to discretize the time and space fractional order operators; the first order space derivative is discretized using the central difference quotient. The TFCGMY model and the above numerical techniques are used for the pricing analysis of European call options. By comparing and analyzing the option pricing model with the Black-Scholes model and the CGMY model shows that the introduction of time fractional differentiation can better capture the jump characteristics of stock prices of options.