Resilience of Volatility

TL;DR

This paper investigates the non-stationarity of financial market volatility, proposing a new measure for current volatility estimation, and demonstrates that removing non-stationarity reduces autocorrelations and kurtosis, aligning distributions closer to Gaussian.

Contribution

It introduces a novel volatility measure, provides a statistical criterion for smoothing, and supports the hypothesis of non-stochastic, smoothly varying volatility in financial markets.

Findings

Removing non-stationarity reduces autocorrelations in volatility.

Eliminating non-stationarity decreases distribution kurtosis.

Proposed measure improves current volatility estimation.

Abstract

The problem of non-stationarity in financial markets is discussed and related to the dynamic nature of price volatility. A new measure is proposed for estimation of the current asset volatility. A simple and illustrative explanation is suggested of the emergence of significant serial autocorrelations in volatility and squared returns. It is shown that when non-stationarity is eliminated, the autocorrelations substantially reduce and become statistically insignificant. The causes of non-Gaussian nature of the probability of returns distribution are considered. For both stock and currency markets data samples, it is shown that removing the non-stationary component substantially reduces the kurtosis of distribution, bringing it closer to the Gaussian one. A statistical criterion is proposed for controlling the degree of smoothing of the empirical values of volatility. The hypothesis of smooth, non-stochastic nature of volatility is put forward, and possible causes of volatility shifts are discussed.