Pricing of basket options in subdiffusive fractional Black-Scholes model

In this paper we generalize the classical multidimensional Black-Scholes model to the subdiffusive case. In the studied model the prices of the underlying assets follow subdiffusive multidimensional geometric Brownian motion. We derive the corresponding fractional Fokker-Plank equation, which describes the probability density function of the asset price. We show that the considered market is arbitrage-free and incomplete. Using the criterion of minimal relative entropy we choose the optimal martingale measure which extends the martingale measure from used in the standard Black-Scholes model. Finally, we derive the subdiffusive Black-Scholes formula for the fair price of basket options and use the approximation methods to compare the classical and subdiffusive prices.