A fast Monte-Carlo simulation algorithm based on geometric Brownian motions and its application

Due to the non-standardized feature of most options, their pricing models have no closed solution. Therefore, it is important to develop the numerical algorithms to obtain the options fair value. In this paper we propose a fast Monte-Carlo simulation algorithm based on data driven. First, we introduce geometric Brownian motions to describe the price feature of the underlying asset and proposed the options pricing model under the risk-neutral measure. Then, to solve the pricing model for the options, a fast Monte Carlo simulation algorithm is proposed. Finally, through numerical examples, we display how to obtain the option price by the fast Monte-Carlo simulation algorithm.