Asian option pricing under sub-fractional vasicek model

Abstract

This paper investigates the pricing formula for geometric Asian options where the underlying asset is driven by the sub-fractional Brownian motion with interest rate satisfying the sub-fractional Vasicek model. By applying the sub-fractional $ {\rm{It\hat o}} $ formula, the Black-Scholes (B-S) type Partial Differential Equations (PDE) to Asian geometric average option is derived by Delta hedging principle. Moreover, the explicit pricing formula for Asian options is obtained through converting the PDE to the Cauchy problem. Numerical experiments are conducted to test the impact of the stock price, the Hurst index, the speed of interest rate adjustment, and the volatilities and their correlation for the Asian option and the interest rate model, respectively. The results show that the main parameters such as Hurst index have a significant influence on the price of Asian options.