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Asymmetric relationship between price and volatility is a prominent featureof the financial market time series. This paper explores the price-volatilitynexus in cryptocurrency markets and investigates the presence of asymmetricvolatility effect between uptrend (bull) and downtrend (bear) regimes. Theconventional GARCH-class models have shown that in cryptocurrency markets,asymmetric reactions of volatility to returns differ from those of othertraditional financial assets. We address this issue from a viewpoint of fractalanalysis, which can cover the nonlinear interactions and the self-similarityproperties widely acknowledged in the field of econophysics. The asymmetriccross-correlations between price and volatility for Bitcoin (BTC), Ethereum(ETH), Ripple (XRP), and Litecoin (LTC) during the period from June 1, 2016 toDecember 28, 2020 are investigated using the MF-ADCCA method and quantified viathe asymmetric DCCA coefficient. The approaches take into account thenonlinearity and asymmetric multifractal scaling properties, providing newinsights in investigating the relationships in a dynamical way. We find thatcross-correlations are stronger in downtrend markets than in uptrend marketsfor maturing BTC and ETH. In contrast, for XRP and LTC, inverted reactions arepresent where cross-correlations are stronger in uptrend markets.

Exploring asymmetric multifractal cross-correlations of price-volatility and asymmetric volatility dynamics in cryptocurrency markets