Stochastic volatility and transaction time: an activity-based volatility estimator

Thierry Ané, Hélyette Geman

Abstract

ABSTRACT

A number of different specifications of stochastic volatility have been suggested to describe the empirical leptokurtic distributions of stock returns. Geman and Ané have shown that the nonnormality of asset returns exhibited on a high-frequency database of equity indexes can be corrected through a renormalization of time, namely by the use of a stochastic clock directed by the number of trades. Building on this research, the authors introduce in this paper a so-called activity-related volatility estimator. It is established that this estimator is a better predictor of future realized volatility than the historical volatility, which in turn is itself superior to the implied volatility.