Modeling the tail risk of crude oil futures using a quantum approach

Abstract This study proposes a quantum approach to measure the tail risk of crude oil futures. Based on the quantum harmonic oscillator (QHO) model, we first model the log return process of crude oil futures. From the equilibrium distribution of QHO model, we calculate the well-known tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES); we confirm that this quantum approach provides precise estimates of in-sample and out-of-sample VaR and ES for crude oil futures. The findings suggest the QHO model for log return process outperforms the geometric Brownian motion for price process and the historical simulation approach. The excellence of QHO model in explaining the tail risk of crude oil futures can be attributed to its fast angular frequency and high probability allocation in excited states. Crude oil market participants can use this study’s analytical framework to precisely measure and manage potential risks in the marketplace. Regulatory authorities can evaluate the degree of crude oil market instability through the current market state of crude oil futures characterized by the QHO model parameters while devising and revising crude oil market regulations. Future research can examine quantum models with (1) different assumptions, e.g., position-dependent diffusion and time-varying equilibrium return, and (2) different potential functions, e.g., infinite and finite square well.