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.