A lognormal/normal regime-switching commodity pricing model

Abstract

Inspired by the negative price of WTI crude oil observed during the COVID-19 pandemic, we develop a new model for commodity pricing which allows structural change between price normality and lognormality under a Markov regime-switching (RS) framework. We augment the Extended Kalman Filter to calibrate the structural changing model. The model performance in calibration is compared to that of the common RS model with historical WTI spots, various futures and hypothetical scenarios. We conclude that our model is superior in capturing price dynamics especially in the oil market downturns. Encouragingly, the regime probabilities estimated with the new model indicate that during severe events including the 2008–2010 financial crisis, 2014–2016 oil crash and the outbreak of COVID-19 in 2020, WTI spot itself follows normal rather than the widely assumed lognormal process. This finding is consistent with our empirical studies. In addition, we assess the probability density of spot prices with the new model. Finally, we present the PDE finite difference and Monte Carlo approaches to price commodity options under the new model.