We explore the scaling properties of price-volatility nexus in cryptocurrency markets and address the issue of the asymmetric volatility effect within a framework of fractal analysis . The MF-ADCCA method is applied to examine nonlinear interactions and asymmetric multifractality of cross-correlations between price and volatility for Bitcoin  , Ethereum, Ripple, and Litecoin . Furthermore, asymmetric reactions in the volatility process to price fluctuations between uptrend (bull) and downtrend (bear) regimes are discussed from the viewpoint of cross-correlations quantified by the asymmetric DCCA coefficient , which is a different approach from the conventional GARCH-class models . We find that cross-correlations are stronger in downtrend markets than in uptrend markets for maturing Bitcoin and Ethereum . In contrast, for Ripple and Litecoin , inverted reactions are present where cross-correlations are stronger in uptrend markets . Our empirical findings uncover the dynamics of asymmetric volatility structure and provide new guidance in investigating dynamical relationships between price and volatility for cryptocurrencies .
Asymmetric relationship between price and volatility is a prominent feature of the financial market time series. This paper explores the price-volatility nexus in cryptocurrency markets and investigates the presence of asymmetric volatility effect between uptrend (bull) and downtrend (bear) regimes. The conventional GARCH-class models have shown that in cryptocurrency markets, asymmetric reactions of volatility to returns differ from those of other traditional financial assets. We address this issue from a viewpoint of fractal analysis , which can cover the nonlinear interactions and the self-similarity properties widely acknowledged in the field of econophysics. The asymmetric cross-correlations between price and volatility for Bitcoin (BTC), Ethereum (ETH), Ripple (XRP) , and Litecoin (LTC) during the period from June 1, 2016 to December 28, 2020 are investigated using the MF-ADCCA method and quantified via the asymmetric DCCA coefficient . The approaches take into account the nonlinearity and asymmetric multifractal scaling properties, providing new insights in investigating the relationships in a dynamical way . We find that cross-correlations are stronger in downtrend markets than in uptrend markets for maturing BTC and ETH . In contrast, for XRP and LTC , inverted reactions are present where cross-correlations are stronger in uptrend markets .
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