Quantile Dependence between Crude Oil Returns and Implied Volatility: Evidence from Parametric and Nonparametric Tests

Abstract

We examine the daily dependence and directional predictability between the returns of crude oil and the Crude Oil Volatility Index (OVX). Unlike previous studies, we apply a battery of quantile-based techniques, namely the quantile unit root test, the causality-in-quantiles test, and the cross-quantilogram approach. Our main results show evidence of significant bi-directional predictability that is quantile-dependent and asymmetric. A significant positive Granger causality runs from oil (OVX) returns to OVX (oil) returns when both series are in similar lower (upper) quantiles, as well as in opposite quantiles. The Granger causality from OVX returns to oil returns is only significant during periods of high volatility, although it is not always positive. The findings imply that the forward-looking estimate of oil volatility, reflecting the sentiment of oil market participants, should be considered when studying price variations in the oil market, and that crude oil returns can be used to predict oil implied volatility during bearish market conditions. Therefore, the findings have implications regarding predictability under various conditions for oil market participants.

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“…The Mann-Kendall test is a non-parametric statistical test used to identify monotonic trends in data [35]. It calculates the Kendall Tau, reflecting the strength and direction of the trend, and the Sen's Slope, quantifying the magnitude of temporal change [36][37][38]. Calculations of the Kendall Tau and Sen's Slope were performed using the Google Earth Engine, leveraging the capabilities provided by the platform (https://developers.google.com/earth-engine/tutorials/ community/nonparametric-trends, accessed on 15 January 2022).…”

“…The use of Kendall Tau in trend analysis offers certain advantages compared to linear regression and developed by Kendall represented in Equation ( 2) [39]. Unlike linear regression, Kendall Tau is not affected by the presence of outliers and data errors, making it robust for detecting monotonic patterns in the data [36][37][38]. The formula of calculating Kendall Tau is:…”