Stein's Overreaction Puzzle: Option Anomaly or Perfectly Rational Behavior?

Abstract

Empirical studies have shown that implied volatilities of long-term options react quite strongly to changes in implied volatilities of short-term options and do not display the rationally expected smoothing behavior. Given the observed strong mean-reversion in volatility, those findings have been interpreted as evidence for overreaction in the options market. Focusing on a stochastic variance process in a rational expectation framework, we theoretically show that under normal market conditions the risk-neutral volatility dynamics are substantially more persistent than the physical one. As a result, the empirical observation of a strong reaction of long-term volatility would be consistent with perfectly rational behavior. We additionally show that the degree of persistence depends on investors’ risk aversion. Using daily data on S&P 500 index options, we confirm previous findings for the 2000-2010 period, which is characterized by an overall moderate level of risk aversion. Once we identify periods of high and low risk aversion, in line with the predictions of our theoretical model, empirical results only hold for periods, when investors are highly risk averse. During periods of low risk aversion, results are insignificant. Robustness checks reveal that the results are remarkably stable over the complete term structure. Therefore, we provide strong evidence that the empirical observation is not overreaction, but in line with perfectly rational behavior.