Empirical Evidence on Volatility Estimators

by João Duque of the Universidade Técnica de Lisboa, and
Dean A. Paxson of the University of Manchester

May 1997

Abstract: Are historical volatilities better then implied volatilities in estimating future (also known as actual or realised) volatilities? Which method of measuring historical or implied volatility is best? In this paper we discuss the methodology for calculating these approaches to volatility, carry out empirical tests on each estimator, as well as on their interrelations.

In order to test the "quality" of the estimators, comparisons among historical, implied and future volatilities were used for a full range of estimators. This identifies some of the criticisms for each estimator. The differences found among different estimators are statistically significant and should became fully noted by users of volatilities in the pricing and trading "volatility dependent securities" such as options. Moreover we observed some empirical evidence of the so-called "smile effect" that explains why implied volatility estimators that embody the moneyness effect show lower errors in predicting future volatilities. We also found some empirical evidence for the increase of the smile effect with the approach of the maturity. We also found that the selection of a specific estimator can lead to biased conclusions when studying the forecast ability of implied volatilities. Finally the exercise price effect seems to be asymmetrically dependent on stock price changes.

JEL Classification: N2.

Keywords: Volatility estimators, implied volatility, historical volatility, efficiency.

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