Dynamic return-volatility dependence and risk measure of CoVaR in the oil market: A time-varying mixed copula model

- Dynamic mixed copula model is built to explore risk spillover between WTI and OVX.
- The dynamic and asymmetric dependence between WTI and OVX is studied.
- WTI and OVX present negative dependence most of the time, but not always negative.
- Risk spillover from OVX to WTI is significant under the extreme condition.
- OVX is verified as a gauge of investor fear instead of risk preference.

This study investigates the risk level in the oil market measured by Value-at-Risk (VaR) and conditional VaR (CoVaR), as well as the dynamic and asymmetric dependence between WTI returns and crude oil volatility index (OVX), by constructing six time-varying mixed copula models. Results show that mixed copula between t copula and the 270-degree rotated Clayton copula is the optimal fitting copula to measure dynamic dependence. The estimated time-varying Kendall coefficients indicate that WTI returns and OVX present negative dependence most of the time. There exists a structural change point of dependence between WTI returns and OVX changes on April 17, 2009, while the dependence characteristics within the subsamples are similar to that in the whole sample, indicating the rationality of our time-varying mixed copula models. Finally, the tests show significant risk spillover from OVX to WTI returns and also asymmetric effects for CoVaRs in response to different upside and downside extreme OVX movements.