Fuzzy simulation of European option pricing using sub-fractional Brownian motion

Abstract

On the basis of the sub-fractional Black-Scholes model, considering that the financial market is uncertain with randomness and fuzziness, we used stochastic analysis, fractal theory and fuzzy set theory to construct European option pricing model based on the long-term memory property of the financial market in an uncertain environment. Afterwards the influence of Hurst index H, a measure of long-term memory in financial market, on European option pricing is analyzed. Finally, the rationality and feasibility of the pricing model are demonstrated by numerical experiment. The obtained results show that the European options pricing model with long-term memory property is more suitable for financial markets under uncertain environment.