Pricing European option with the short rate under Subdiffusive fractional Brownian motion regime

The purpose of this paper is to analyze the problem of option pricing when the short rate follows subdiffusive fractional Merton model. We incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formula for call and put option and discuss the corresponding fractional Black-Scholes equation. We present some properties of this pricing model for the cases of $\alpha$ and $H$. Moreover, the numerical simulations illustrate that our model is flexible and easy to implement.