Realized-to-implied volatility ratio and its mean reversion

Abstract

The purpose of this study is to investigate the relationship between the realized volatility and implied volatility. The relationship is investigated through the behavior of a ratio constructed by using the implied volatility as the denominator and the realized volatility as the numerator, with the focus on the mean reverting behavior of the volatility ratio. Also the information content of the volatility ratio on the future movements of the ratio components is investigated. This investigation is conducted through Granger causality tests and the investigation of particular trading signals based on the movements of the volatility ratio. The data consists daily realized and implied volatilities of 12 different stocks, and their corresponding options, from the German equity and derivatives markets for the time period from January 1998 to December 2001.

The results support the hypothesis of the mean reversion property of the volatility ratio and the mean reversion is showed to be really quick with the half-life of the shock being on average less than one trading day. The results indicate that the mean reversion of the volatility ratio is driven by the movements on the realized volatility. The results also indicate that the volatility ratio contains information about the future movements of the realized volatility, while it does not contain predictive information on the implied volatility.