Modelling high frequency crude oil dynamics using affine and non-affine jump–diffusion models

This paper investigates the dynamics of high frequency crude oil markets proxied by the United States Oil (USO) exchange traded fund (ETF). USO returns are modelled using a stochastic framework with jumps and stochastic volatility (SVCJ). We consider three nested models within the affine SVCJ framework, and extend our analysis to three additional models within the non-affine framework. We compare six modelling frameworks (affine/non-affine and with/without jumps) based on their ability to capture high frequency USO dynamics. The modelling parameters are estimated using the Particle Markov Chain Monte Carlo (PMCMC) approach. We investigate whether jumps in USO returns and volatility are important, and whether it is necessary to leave the affine model class for the non-affine frameworks when jumps are included in the model. Using various statistical criteria and based on volatility forecasting performance, we document that (i) jumps in the returns and stochastic volatility are essential when modelling USO dynamics; (ii) the non-affine specifications are preferred to the affine specifications: The non-affine SVCJ-NL and SVJ-NL models stand out when modelling high frequency USO returns, followed by the affine SVCJ-L and SVJ-L models. The latter might be better suited for theoretical finance applications, such as derivative pricing, as closed form solutions for option prices are available under the affine frameworks.