Pricing of Asian Options Based on Time-Changed Mixed Fractional Brownian Motion

In this paper, the pricing problem of geometric average Asian options under the Vasicek interest rate based on a time-changed mixed fractional Brownian motion is considered. A stochastic process similar to the renewal process is applied to characterize the constant periodicity of the financial asset price in emerging financial markets. The time-changed mixed fractional Brownian motion model Mα ,H(t) = aB(T_α (t)) + bBH(T_α (t)) is introduced to describe the underlying asset process of Asian options. When the Hurst exponent satisfies certain conditions, the model is used to price options without arbitrage. By using the hedging and no-arbitrage principle, the partial differential equation satisfied by the price of an Asian option is given. The pricing formula of an Asian call and a put option, and the corresponding parity formula, are obtained, along with their explicit solution.