Author(s)

Guanhao Hua, Linfeng Sun, Hsuan Wu

Corresponding Author

Guanhao Hua

ABSTRACT

Multi-asset options have many advantages over individual derivative options such as allowing investors to hedge against multiple risks and reducing transaction costs. Based on the price of gold and crude oil from 1986 to 2021, Geometric Brownian Motion Model (GBM) is introduced to predict gold Future price paths and WTI crude price paths. This article assumes that commodity prices exhibit randomness that can be explained and modeled by the GBM model and use the GBM model to simulate the future price paths for gold and WTI crude oil. To account for the correlation, the GBM of the second asset is modified. Then the average payout is determined and used as the estimator for the call price of the European basket option. Finally, sensitivity analysis is done by examining the following variables: correlation, risk-free rate, and volatility. As correlation decreases from positive to negative, the price of the call basket option also decreases. If the relationship between Gold and WTI crude has truly become decoupled in recent years then a call basket option of Gold and WTI crude will be cheaper and accessible to investors.

KEYWORDS

Geometric Brownian Motion (GBM)