The Price of the Smile and Variance Risk Premia

Abstract

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a downward sloping term structure of low-frequency variance risk premia in normal times. In periods of distress, the term structure is upward sloping and dominated by a high-frequency premium for jump variance. This dichotomy is consistent with the puzzling skew sensitivities of option markets with credit-constrained intermediaries and it builds a challenge for many reduced-form and structural models of stochastic volatility.

Keywords: Price of the Smile, Price of Volatility, Option Pricing, Stochastic Volatility, Unspanned Skewness, Financial Constrains, Financial Intermediation, Financial Crisis, Factor Models, Matrix Jump Diffusions, Variance Swaps, Skew Swaps

JEL Classification: G10, G12, G13