  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.
