Hurst Exponent Analysis: Evidence from Volatility Indices and the Volatility of Volatility Indices

Abstract

In this study, we analyze the volatility of volatility indices and estimate the Hurst parameter using data from five international markets. For our analysis, we consider daily data from VIX (CBOE), VXN (CBOE Nasdaq 100), VXD (DJIA), VHSI (HSI), and KSVKOSPI (KOSPI). The period of analysis is from January 2001 to December 2021 and incorporates various market phases, such as booms and crashes. The novelty here is the use of recent methodology, including different range-based estimators for volatility analysis. We apply the Hurst exponent to the volatility measures Vgk,t, Vp,t, Vrs,t, and Vs,t, and then estimate the volatility of volatility indices through the GARCH(1, 1) model. Based on the values of the Hurst exponent, we analyze the trace of the behavior of three trading strategies, i.e., the momentum-based strategy, the random walk, and the mean-reversion strategy. The results are highly recommended for financial analysts dealing with volatility indices as well as for financial researchers.