Narrow Results

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.

The fall of crude oil futures into extreme negative prices has raised concerns globally. On the one hand, although the negative price mechanism facilitates market price discovery to some extent, in the delivery month it can trigger serious consequences such as abnormal market price fluctuations due to insufficient liquidity, which creates extreme market injustice and raises suspicion of manipulation. On the other hand, the reckless change of programs, which allow negative prices, lacks necessary legitimacy at the procedural level. Market participants who have been treated unfairly should actively defend their rights, and United States regulators and the Chicago Mercantile Exchange Group Inc. (CME) should explain to the market with thorough investigations and credible conclusions. The negative oil price incident is a profound warning and lesson for financial institutions and regulators in China.

Fischer Black and Myron Scholes (1973) assumed asset prices follow lognormal distributions and derived the famous Black–Scholes option pricing formula. The lognormal assumption implies the asset price will never be negative and has zero as its lower bound. By relaxing the negative and zero bound, we derive a Black–Scholes-like option pricing formula for asset prices following a shifted lognormal distribution with a lower bound. The formula can be applied to price options with negative prices and negative strikes.