European Option Pricing Under the Vaseck Model of the Short Rate in Mixed Fractional Brownian Motion Environment

Abstract

In this study, assume that the stock price obey the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vaseck model. Then, the Black-Scholes partial differential equation is obtained under the assumptions by using fractional Ito formula. Finally, the pricing formulae of the European call and put option are obtained by partial differential equation theory. The results of Black-Scholes model is generalized.