Disentangling the Contribution of Return-Jumps and Volatility-Jumps : Insights from Individual Equity Options

This article investigates option models in the encompassing class of stochastic volatility, returnjumps, and volatility-jumps. Relying on individual equity options and method of simulated moments estimation, several major results obtained are, first, that the double-jump process is the least misspecified and the least demanding in fitting the tail-size and tail-asymmetry of individual risk-neutral return distributions; second, the double-jump model improves pricing performance beyond return-jumps absent volatility-jumps, and beyond volatility-jumps absent return-jumps; third, between return-jumps and volatility-jumps, the former is empirically more relevant than the latter for pricing options; fourth, the inverse link between volatility-jumps and return-jumps is instrumental for explaining the valuation of deep out-of-money puts and option dynamics of firms with high kurtosis; fifth, stochastic volatility is not as important for individual equity options as it is for index options. Incremental insights that emerge from individual equity options bring clarity to divergent findings on the role of return-jumps and volatility-jumps. Duffie, Pan, Singleton’s (2000) introduction of double-jump stock price dynamics with correlated return-jumps and volatility-jumps has brought the recognition that option model misspecification could be related to the dual character of jumps. This new view from the double-jump model class suggests that inversely-correlated return-jumps and volatility-jumps are capable of internalizing risk-neutral kurtosis and skewness far more effectively than extant models. Refuting this theoretical parameterization however, the empirical results in Eraker (2002) conclude that return-jumps and volatility-jumps are unable to reconcile S&P 500 index option dynamics and the double-jump feature is largely irrelevant beyond stochastic volatility. The jump-irrelevancy result appears surprising and our intent is to provide new insights from individual equity options to bear upon the issue of relative contribution of return-jumps and volatility-jumps. To address existing discrepancies with respect to the role of return-jumps and volatility-jumps, we analyze a large sample of individual equity options. Thus, our results are robust under various combinations of risk-neutral kurtosis and skewness. In addition, our estimation method takes advantage of the time-series information and infers model dynamics by applying method-of-simulated moments (Duffie and Singleton (1993) and Gouriéroux and Monfort (1996)). Model implementation with individual equity options brings clarity to a number of contentious issues. First, the structural parameters obtained from method-of-simulated moments are broadly consistent with negatively correlated volatility-jumps and return-jumps, and option-models excluding a linkage between return-jumps and volatility-jumps are associated with implausible correlation between stock return and volatility. One drawback of alternative option-models is that they can sustain high kurtosis only at the expense of more left-skew which is counterfactual for individual equities. Viewed from the sensibility of imputed parameters and specification analysis, the double-jump process is the least restrictive in fitting individual option prices. While stochastic volatility leads to a first-order improvement in the case of index options, the incremental insight that emerges from individual equity options is that jumps and risk-neutral kurtosis are instrumental to modeling individual option prices. Departing from Eraker (2002) where the worst performing specifications are the stochastic volatility with return-jump model and the double-jump model, our findings strongly support an economic and statistical role for jumps. We show that jump models are necessary to realistically characterize the time-series and moneyness-maturity dimension of individual equity option prices. Novel to our study, the empirical investigation suggests that return-jumps are of a higher-order importance than volatility-jumps. Generalizing the stochastic volatility model to include only return-jumps produces a larger improvement compared to a competing generalization that includes only volatility-jumps. Indicative of misspecified volatility specification, adding orthogonal volatility-jumps beyond return-jumps worsens performance. Thus, price specifications that rely on return-jumps to generate excess