What is the Equilibrium Price of Variance Risk? A Long-Run Risks Model with Two Volatility Factors

Abstract

This paper explores how economic uncertainty evolves over time and how it is priced in the market. We solve for the variance premium, the prices of equity index options, and the prices of volatility related derivatives in a long-run risks model. We find that both short-run and long-run uncertainty factors are necessary to explain the empirical characteristics of variance risk while remaining consistent with consumption and asset pricing data. The variance premium is mainly driven by the risk of a sudden increase in the overall level of uncertainty. Out-of-the-money equity index put options and out-of-the-money call options on variance provide insurance against market crashes. Consistent with the data, these contracts are priced at a premium.

Keywords: long-run risks, variance premium, volatility derivatives

JEL Classification: G12, G13