Empirical analysis of crude oil dynamics using affine vs. non-affine jump-diffusion models

This paper investigates the dynamics of the United States oil (USO) exchange traded fund (ETF). Daily USO returns are modelled using stochastic volatility (SV) frameworks derived from three different model classes: SV models with contemporaneous jumps in returns and volatility (SVCJ); SV model with jumps in returns only (SVJ); and a pure SV model class without jumps. Six affine and non-affine models are considered within each model class that depend on specification of the drift and the diffusion terms in the variance process, resulting in a total of 18 models that are estimated using particle Markov Chain Monte Carlo (PMCMC) approach. Model evaluation is conducted using the Deviance Information Criterion (DIC), Bayes factors, probability plots, and deviation measures to assess the discrepancy between the estimated volatility and key benchmarks, the crude oil ETF volatility index (OVX) and the realised volatility (RV). Our analysis indicates that models incorporating jumps, particularly the SVCJ-PLY-0.5 and SVCJ-PLY-1.0, more accurately capture USO dynamics than standard SV models. The SVCJ-PLY-0.5 model ranks highest based on DIC statistics and Bayes factors, and both models excel in aligning their estimated volatility with the OVX and RV benchmarks. Overall, the statistical criteria employed in our comparison favour models with jumps over the standard SV model class, suggesting that models incorporating jumps in both return and variance processes (SVCJ) are superior to those with jumps solely in the return process (SVJ). The affine models SVJ-LIN-0.5 and SVCJ-LIN-0.5 with linear variance drift and square root diffusion that are particularly interesting for theoretical finance applications are highly ranked among considered frameworks, outperforming several non-affine alternatives. Our analysis of the regression model for volatility forecasting reveals a significant predictive accuracy in the evaluated models, demonstrating their effectiveness in anticipating future volatility trends.