Expected Returns, Risk Premia, and Volatility Surfaces Implicit in Option Market Prices

Abstract

This article presents a pure exchange economy that extends Rubinstein (1976) to show how the jump-diffusion option pricing model of Merton (1976) is altered when jumps are correlated with diffusive risks. All correlations are statistically different from zero. In equilibrium, the equity risk premium depends not only on the risk premium factors of the traditional jump-diffusion models with systematic jump and diffusion risks, but also on both the covariance of the diffusive pricing kernel with price jumps and the covariance of the jumps of the pricing kernel with the diffusive price. These two covariances are positive, and they help to explain the sneers that we observe in the marketplace. The expected stock return is not given by the sum of the diffusive expected return and the expected return due to jumps, but it takes also into account the covariance between the diffusive return and price jumps. Our evidence is consistent with a negative covariance, which leads to a nonmonotonic term structure of implied volatilities. This leads to an asset pricing model and an option pricing model where the level of the market prices is correlated with the size of the jumps.

Keywords: Jump-diffusion, option prices, correlated jumps and diffusions, expected returns, risk premium, smile effect, term structure of implied volatilities

JEL Classification: G12, G13