Pricing of European Option in Sub-factional Brownian Motion with Dividend Payments

In this paper, we establish the option pricing model under sub-fractional Brownian motion, and consider the situation of the continuous dividend payments. Firstly, Wick-It\^o integral and partial differential method are used to get the option price of partial differential equation, and then through variable substitution into Cauchy problem, we can get the pricing formula of European call option with dividend-paying in sub-fractional Brownian motion environment. According to the pricing formula of European call option, the European put option pricing formula is obtained. Moreover, we study the parameter estimation in the model, and consider the unbiasedness and the strong convergence of the estimator.