The Sensitivity of Implied Volatility to Expectations of Jumps in Volatility: An Explanation to the Illusory Bias in Implied Volatility as a Forecast

Abstract

The apparent bias in implied volatility as a forecast of the subsequently realized volatility is a well-documented empirical puzzle. As suggested by e.g. Feinstein (1989), Jackwerth and Rubinstein (1996), and Bates (1997), we test whether unrealized expectations of jumps in volatility could explain this phenomenon. Our findings show that expectations of infrequently occurring jumps in volatility are priced in implied volatility, which has two important consequences. First, implied volatility will slightly exceed realized volatility most of the time only to be considerably lower than realized volatility during infrequently occurring periods of very high volatility. Second, the slope coefficient in the classic forecasting regression of realized volatility on implied volatility is very sensitive to the discrepancy between the ex ante expected and ex post realized jump frequencies. If the in-sample frequency of positive volatility jumps is lower than ex ante assessed by the market, the slope coefficient will be biased downward and the classic regression test will erroneously reject the hypothesis of no bias even if the market is informationally efficient. Since the inferences of almost all previous studies on the forecasting power of implied volatility have been based on data from a period of historically low volatility, our results provide a rational explanation for the illusory bias in implied volatility.