Stock Return Extrapolation, Option Prices, and Variance Risk Premium

Abstract

This paper presents a tractable dynamic equilibrium model of stock return extrapolation in the presence of stochastic volatility. In the model, consistent with survey evidence, following positive (negative) stock returns, investors expect future returns to be higher (lower) but also less (more) volatile. The biased volatility expectation introduces a new channel through which past returns and investor sentiment affect derivative prices. In particular, through this novel channel, the model reconciles the otherwise puzzling evidence of past returns affecting option prices and the evidence of variance risk premium predicting future stock market returns even after controlling for the realized variance.

Keywords: extrapolation, sentiment, stochastic volatility, variance bias, option prices, variance risk premium

JEL Classification: G12, G13