The asymmetric relationship between volatility index and volatility-of-volatility index

Abstract

ABSTRACT We use the nonlinear autoregressive distributed lag model to assess the asymmetric relationship between the Chicago Board Options Exchange’s volatility index (VIX) and volatility-of-volatility index (VVIX) over the period January 2007 to March 2020. To control for potentially confounding factors, we include measures for economic policy uncertainty and the volatility risk premium. There are three key findings. First, we find that there is an asymmetric long run cointegrating positive relationship running from VVIX to VIX. In this long run relationship, VIX is more responsive to deceases in VVIX than increases in VVIX. Second, we also find an asymmetric short run relationship between VIX and VVIX. However, in contrast to the long run results, for the short run VIX is more responsive to increases in VVIX than decreases in VVIX. Third, consistent with other studies, we find that in the long run VIX rises with greater economic policy uncertainty but falls with increases in the volatility risk premium. We discuss the implications of our findings for practitioners in risk and portfolio management, derivative pricing, and trading.