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This paper calibrates a class of jump-diffusion long-run risks (LRR) models to quantify how well they can jointly explain the equity risk premium and the variance risk premium in the U.S. financial markets, and whether they can generate realistic dynamics of risk-neutral and realized volatilities. I provide evidence that the jump risk in volatility of long run consumption growth is a key component of the equity risk premium and the variance risk premium in financial markets. Moreover, I find that matching the VIX dynamics during the calibration process is crucial when comparing different jump channels. Specifically, a jump-in-growth LRR model generates a good fit of the average variance risk premium, but a poor fit of the dynamics of the VIX or realized stock volatility. In contrast, a jump-in-volatility LRR model generates a smaller variance risk premium but better fits the VIX and the realized stock volatility dynamics. Finally, jump-in-volatility models generate predictability of returns by the variance risk premium that is more consistent with the data.

Jump-Diffusion Long-Run Risks Models, Variance Risk Premium, and Volatility Dynamics*