  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.
