We shed light on the nature of jump risk compensation by studying the profits from a trading strategy that bets on the high-frequency jump skew of S&P 500 returns. Earlier evidence suggests the jump risk premium is large and positive. We find it to be concentrated in periods when the index option market is closed, and investors cannot trade options. Whenever jump skew can be traded continuously, the premium vanishes. We conclude the jump skew premium in index options is not compensation for the risk of occasional, large returns, but for the investors’ inability to adjust their nonlinear risk exposure.
We develop a theory of arbitrage-free dispersion (AFD) that characterizes the testable restrictions of asset pricing models. AFD measures Jensen's gap in the cumulant generating function of pricing kernels and returns. It implies a wide family of model-free dispersion constraints, which extend dispersion and co-dispersion bounds in the literature and are applicable with a unifying approach in multivariate and multiperiod settings. Empirically, the dispersion of stationary and martingale pricing kernel components in the benchmark long-run risk model yields a counterfactual dependence of short- vs. long-maturity bond returns and is insufficient for pricing optimal portfolios of market equity and short-term bonds.
The option implied volatility surface can be succinctly summarised by the prices of certain option portfolios, which can be interpreted as the slope of the cumulant generating function of the underlying log return. In affine jump-diffusion models, the prices of some of such contracts are affine in the latent state variables. On the contrary, the prices of options are not. I show that state recovery with full option datasets, even when employing techniques that account for the non-linearity, is inferior to reduced-dimension filters which take the prices of CGF-slope replicating contracts.
We propose a computationally tractable estimation approach for a completely specified (under P and Q) multifactor stochastic volatility model that aims to fit the dynamic properties of returns on option trading strategies. We show in a Monte Carlo experiment that our approach delivers reliable results even under moderate misspecification. We estimate a model using returns on delta-hedged option portfolios as observables. We describe the empirical properties of such returns and recover their model-implied conditional second moment structure. Return-fitted models exhibit lacking pricing properties. Including price information in the estimation significantly worsens the model’s ability to plausibly describe delta-hedged option returns. It is a demanding task for an affine model to reconcile the requirements of the two tasks at hand.