The application of fractional brownian motion in option pricing

Abstract

In this text, Fractional Brown Motion theory during random process is applied to research the option pricing problem. Firstly, Fractional Brown Motion theory and actuarial pricing method of option are utilized to derive Black-Scholes formula under Fractional Brown Motion and form corresponding mathematical model to describe option pricing. Secondly, based on BYD stock, estimation model on volatility of this stock is given to analyze and calculate the stock price volatility. Finally, make instance analysis for BYD’s option. Based on market data of BYD’s stock and option, calculate the actual option price and theoretical price of BYD by Black-Scholes formula under Fractional Brown Motion. Compare the forecast price of this stock option given by model with actual price, relatively good effect is obtained, and then conclude that the model has relatively strong applicability.