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

摘要

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, the authors show that under normal market conditions the risk-neutral volatility dynamics are substantially more persistent than the physical one. Furthermore, they show theoretically that the elasticity of long-term variance depends on investors' risk aversion and, therefore, on the persistence of the volatility process. As a result, the empirical observation of a strong reaction of long-term volatility would be consistent with perfectly rational behavior. They additionally demonstrate that the degree of persistence depends on investors' risk aversion. Using daily data on S&P 500 Index options, the authors confirm previous findings for the 2000-2010 period, which is characterized by an overall moderate level of risk aversion. Once they identify periods of high and low risk aversion, in line with the predictions of their theoretical model, the empirical results of a strong reaction of long-term variance only hold for periods when investors are highly risk averse. During periods of low risk aversion, the effect is insignificant. Therefore, they provide strong evidence that the empirical observation is not overreaction but in line with perfectly rational behavior.