ABSTRACT We have conducted a thorough analysis of four stochastic volatility models, including double exponential jumps and infinite-activity Lévy jumps. By selecting recent data from Shanghai crude oil futures and Brent crude oil, we explore the impact of the COVID-19 pandemic and characterized the price fluctuations in the Shanghai crude oil market. We estimate the model parameters using the MCMC method and discuss the significance of jumps in crude oil futures returns. Our study provides evidence that the double exponential jump model is more sensitive to asset price fluctuations and shocks and can better capture the price dynamics of the crude oil market.