We show that market volatility of volatility is a significant risk factor that affects index and volatility index option returns, beyond volatility itself. The volatility and volatility of volatility indices, identified model-free as the VIX and VVIX, respectively, are only weakly related to each other. Delta-hedged index and VIX option returns are negative on average and are more negative for strategies that are more exposed to volatility and volatility-of-volatility risks. Further, volatility and volatility of volatility significantly negatively predict future delta-hedged option payoffs. The evidence suggests that volatility and volatility-of-volatility risks are jointly priced and have negative market prices of risk.

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Abstract. This paper reviews the status quo of the empirical literature about the elasticity of intertemporal substitution (EIS) in consumption. Aiming to answer the question what the true magnitude of the parameter really is, it discusses several recent advances of the theory and highlights challenges for the estimation. Although the general discussion still seems to be prevailed by Hall's early EIS estimates close to zero, we show that several deviations from the time-additive constant relative risk aversion model speak in favor of considerably higher values. Our treatment is supposed to provide researchers a hint at which parameter is a reasonable and incontrovertible choice for the calibration of models in macroeconomics and finance.

This internet appendix provides information on summary statistics, the estimation technique, as well as on the simulation study that are not contained in the paper.Section 1 comprises a table with summary statistics of the data used in the paper.Section 2 describes how we estimate the model parameters and conduct tests with GMM. In Section 3, we briefly review the long-run risks model and its solution.We then discuss the conditional expected value, a key feature of the smooth ambiguity model. Afterwards, we extensively discuss the finite sample properties of our estimation technique based on simulated data.