Abstract
Unlike previous studies that consider the Chicago Board of Options Exchange (CBOE) implied volatility index (VIX), we examine long memory and fractality in the universe of nine CBOE volatility indices. Using daily data from October 5, 2007, to October 5, 2020, covering calm and crisis periods, we find evidence of long memory and fractality in all indices and a change in the degree of volatility persistence, which points to inefficiency. The long memory of the SKEW index is strong before the onset of three crisis periods, but eases afterwards. The findings provide new insights that matter to investment decisions and trading strategies.
Highlights
Within the basis of the efficient market hypothesis (EMH) of Malkiel and Fama [1], the weak form efficiency hypothesis points to the inability of investors to exploit information from historical prices to earn consistent abnormal profits
Our goal is to extend the scarce literature by Hurst exponent using the autoregressive fractionally integrated moving average (ARFIMA) model considering the wide universe of volatility indices covering volatility index (VIX), VXN, VXO, VXD, RVX, VIX Premium Strategy Index (VPD), OVX, volatility of the VIX (VVIX), and SKEW
Past levels in the volatility index have a significant impact on current levels, suggesting that correlations between levels decay very slowly. e results indicate the presence of the long-memory effect in all volatility indices
Summary
Within the basis of the efficient market hypothesis (EMH) of Malkiel and Fama [1], the weak form efficiency hypothesis points to the inability of investors to exploit information from historical prices to earn consistent abnormal profits. Implied volatility indices are established to reflect investor psychology, and, the volatility tracking and the pattern identification become quite pertinent In this regard, the fractal market hypothesis (FMH), developed by Peters [7], relies upon investor behaviour contrary to the EMH that considers investors to be rational (previous studies consider the presence of long-term memory properties to make inferences in favour of the FMH and the possibility of predicting stock prices). The fractal market hypothesis (FMH), developed by Peters [7], relies upon investor behaviour contrary to the EMH that considers investors to be rational (previous studies consider the presence of long-term memory properties to make inferences in favour of the FMH and the possibility of predicting stock prices) In this regard [8], the Hurst exponent is widely used to measure long-term memory properties through its ability to quantify the degree of persistence of similar price change patterns
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