Nonparametric jump variation measures from options

This paper proposes a novel nonparametric method for estimating tail jump variation measures from short-dated options, which can achieve rate-efficiency and works in a general infinite jump activity setting, avoiding parametric or semiparametric assumptions for the jump measure. The method is based on expressing the measures of interest as integrals of the Laplace transforms of the jump compensator and developing methods for recovering nonparametrically the latter from the available option data. The separation of volatility from jumps is done in a novel way by making use of the second derivative of the Laplace transform of the returns, de-biased using either the value of the Laplace transform or of its second derivative evaluated at high frequencies. A Monte Carlo study shows the superiority of the newly-developed method over existing ones in empirically realistic settings. In an empirical application to S&P 500 index options, we find risk-neutral negative market tail jump variation that is on average smaller than previous estimates of it, is generated by smaller-sized jumps, and has less dependence on the level of diffusive volatility.