A time-varying jump tail risk measure using high-frequency options data

The nonparametric jump risk measures are sometimes difficult to construct using only the daily closing quotes and prices of short-dated and deep-out-of-the-money options. In this case, a time-varying shape parameter of risk-neutral jump tails in asset returns is usually assumed to be constant from week to week, in order to mitigate the impact of noise. In this context, this study proposes a method for measuring the daily option-implied jump tail risks. We use high-frequency options data with a data cleaning process, which relaxes the constancy assumption to more general cases such that the shape parameter can change at a daily frequency. We also apply the proposed daily tail measure to the high-frequency data of Nikkei 225 options. The results confirm the coherence of the daily tail risk measure with the existing measures but reveal relatively large spikes on particular days during the week associated with the tail events. To demonstrate the usefulness of the proposed measure, we empirically analyze the short-term predictability of the variance risk premium (VRP). The analyses suggest that the daily tail risk measure, which is a jump tail risk component of $${\textit{VRP}}$$ VRP , has a significant predictive power for future $${\textit{VRP}}$$ VRP and that the inclusion of the diffusive and jump risk components of $${\textit{VRP}}$$ VRP as separate predictors improves the forecasting accuracy.