An empirical study of down-and-out put option pricing based on Geometric Brownian Motion and Monte Carlo Simulation: evidence from crude oil and E-mini Nasdaq-100 futures

Abstract

Option, an instrument of significant financial values in the modern market, is of growing importance. In the case of pricing the option, pricing exotic option remains the problem, since none of the practical methods have been developed as a corresponding way of solution. In order to address the existing issue, this paper examines the feasibility of down-and-out put option pricing based on Geometric Brownian Motion and Monte-Carlo Simulation. Specifically, the stock prices will be calculated through the Geometric Brownian Motion certain while the underlying asset price and down-and-out put option price will be obtained by Monte-Carlo simulations. Two typical underlying assets are selected as the investigation target to validate the pricing feasibility: Crude Oil Futures and E-mini Nasdaq-100 futures. According to the analysis, the barrier option price is lower than a European option, and the barrier option is always cheaper than a European option with the same parameters. These results shed light on the seeking of a method in pricing exotic options.