An S-Shaped Crude Oil Price Return-Implied Volatility Relation: Parametric and Nonparametric Estimations

Abstract

Oil market movements have important implications for portfolio management and hedge strategies for investors who negotiate this commodity. Studies involving the relation of the CBO Crude Oil ETF Volatility Index (OVX) and the United States Oil Fund (USO) return are small in number and do not explore some aspects related to the asymmetry and nonlinearity of this relation. Therefore, this article proposes an analysis about the relation between return and volatility, using parametric and nonparametric methods. To do so, a daily data series from 2007 to 2016, ordinary least squares, quantile regressions and the nonparametric B-splines methods were used. The results indicated a negative, asymmetric and nonlinear contemporary relation between the variables. The effects of negative returns were more pronounced than the positive ones in volatility. In addition, it was found that the relation is not the same for different quantiles. Nonparametric estimates suggested that the positive returns have a convex profile and the negative returns have a concave profile. It indicated the downward-sloping reclined S-curve for the 0.05, 0.90 and 0.95 quantiles of volatility.

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

“…Broadly, our findings prove that the relationships between OVX and oil prices exhibit heterogeneous behavior across quantiles and asymmetric dependence. These findings are partly in line with Agbeyegbe [41], Chen and Zou [57], Silva Junior [45], Lin and Tsai [40], Shaikh [44], and Fousekis [46], who show evidence of asymmetric relationships between OVX and oil prices. Furthermore, our findings are partly in accordance with Aboura and Chevallier [38], who establish the existence of an inverse leverage effect, which characterizes a larger increase in volatility following an upsurge in oil prices than following a decrease in oil prices of the same magnitude.…”

“…They reveal that increasing OVX exhibits a larger negative influence on oil prices than declining OVX, indicating the existence of a long-run asymmetric cointegrating relationship between them. It is worth mentioning that this result of asymmetry is also recognized in previous findings [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Furthermore, Shaikh [44] uses neural network and quantile approaches and suggests that crude oil prices are aligned with OVX.…”

“…They note the presence of significant risk flows from OVX to WTI. In an analogous manner, Silva Junior [45] studies the relationship between United States Oil Fund (USO) returns and OVX, employing ordinary least squares (OLS), quantile regressions (QR), and the nonparametric B-splines regression model. The results show a negative, asymmetric and nonlinear contemporary relationship between the two series, that the effects of negative shocks in volatility are more obvious than positive shocks, and, excitingly, the association has no homogeneous behavior across the various quantiles.…”

“…In this regard, most studies examine the linear relationship between oil returns and OVX (e.g., [38][39][40]), whereas fewer consider the non-linear dependence. Agbeyegbe [41], Ji and Fan [27], Liu et al [21], and Echaust and Just [42] use approaches based on copula models; Li et al [43] apply a multiscale multivariate multifractal detrended fluctuation analysis; and Shaikh [44], Silva Junior [45], and Fousekis [46] use approaches based on quantile regression methods. Nevertheless, none of these studies assess the Granger causal relationship between crude oil returns and OVX based on quantilebased techniques accounting for various market conditions.…”