Valuation of option price in commodity markets described by a Markov-switching model: A case study of WTI crude oil market

Abstract

This paper suggests a Markov-switching model to evaluate commodity futures and spot dynamics, such that the diffusion coefficients and jump size parameter are associated with a hidden Markov chain. We improve the current models in the literature of the commodity markets by modeling the sudden jumps in the commodity prices through the hidden Markov chain. From the crude oil spot price in West Texas Intermediate, we estimate the parameters of proposed Markov-switching model based on expectation–maximization algorithm. To perform this task, we apply this estimation algorithm to the model discretized by Euler scheme and provide some convergence analysis for this discretization method. There are options, such as European options, which are written on the commodity futures. In this study, we evaluate them under the regime-switching model with various economic states. In the following, we calibrate the option prices resulting from the proposed commodity model to a set of observed European call options written on crude oil futures. For this purpose, we first apply an inverse Fourier transform and obtain a semi-analytical option pricing formula. Then, we use the fast Fourier transform method to compute option prices. Since the investors need to calculate Greeks in order to understand the risk involved in option investments, the Greek formulas of Delta, Rho, Theta, and Gamma are derived.