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

Abstract

Among the many anomalies researchers have uncovered in financial markets is Stein’s finding that implied volatilities (IVs) from long-term options are too sensitive to short-shortrun volatility shocks. Option investors overreact to a spike in implied volatility for nearby contracts, and volatilities rise across the maturity spectrum, in contradiction to the smoothing effect when a mean-reverting time series is averaged over a long period. Lehnert, Lin, and Martelin have found a plausible explanation in the fact that mean-reversion of volatility estimated from stock returns is an empirical estimate, while implied volatilities are risk-neutralized values. They show that risk-neutral mean reversion is much slower than in the empirical process. Moreover, it depends on investors’ risk aversion, so that the “overreaction” effect caused by sluggish reversion toward long-run average volatility should be greatest when investors are most averse to risk. They then demonstrate that the theoretical argument is supported by the data. Long-maturity options show significant overreaction to short-maturity IV changes, but the effect is much stronger during periods of market upset. The options market appears to be more rational than Stein’s results suggest.