Presentation slides given at the AMP departmental seminar, May 31, 2021. Shunji Kakinaka is a PhD student with the Physical Statistics Research Group, Department of Applied Mathematics and Physics (AMP), Graduate School of Informatics, Kyoto University. Abstract: Asymmetric correlation between price and volatility is a prominent feature of financial market time series. In this short presentation, the stylized facts of the relationship between price and volatility in cryptocurrency markets are introduced. In addition, the presence of asymmetric volatility effect between uptrend (bull) and downtrend (bear) regimes are investigated using the nonlinear cross-correlation coefficient measures.

1. Asymmetric volatility dynamics in
cryptocurrency markets
Shinji Kakinaka
Applied Mathematics and Physics, Physics Statistics Laboratory
May 31, 2021

2. ▶ Behaviors in financial systems are widely acknowledged as extremely complex.
▶ Recently, research on cryptocurrency market behaviors is becoming an area of
great interest due to the boom.
▶ correlation studies of financial time series play an important role in portfolio
asset allocation as well as risk hedging.
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3. Properties of price fluctuations
▶ returns (price-changes) have no autocorrelation.
▶ the distribution of returns have fat-tails.
▶ generally not a random walk behavior but exhibits multifractal nature.
■ correlation in return series (data obtained from https://poloniex.com/)
2017 2018 2019 2020 2021
Date
0.5
0.4
0.3
0.2
0.1
0.0
0.1
0.2
return
BTC
0 10 20 30 40 50
lags (daily)
0.0
0.2
0.4
0.6
0.8
1.0
correlation
Autocorrelation
▶ No obvious autocorrelation can be seen for returns.
−→ However, absolute values of returns have significant correlations.
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4. Properties of volatility fluctuations
Volatility: dispersion of returns
ex) stv or variance of returns; realized volatility (RV); bipower RV (BPV) etc..
▶ the absolute value of returns have long-range correlation (long-memory).
▶ the distribution do not present fat-tails, but not gaussian.
▶ generally exhibits multifractal nature.
■ long-memory in volatility (data obtained from https://poloniex.com/)
2017 2018 2019 2020 2021
Date
0.00
0.05
0.10
0.15
0.20
0.25
volatility
(BPV)
BTC
0 10 20 30 40 50
lags (daily)
0.2
0.0
0.2
0.4
0.6
0.8
1.0
correlation
Autocorrelation
▶ “volatility” have significant long-range correlations.
−→ correlation patterns exist in the background of price fluctuations.
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5. asymmetric cross-correlations between price and volatility
Conditional variance of equity returns are more affected by negative news
compared to positive news. 1
asymmetric volatility effect
▶ negative returns increase the volatility by more than positive returns
▶ if positive returns increase volatility more, then inverse-asymmetric
This effect is due to the trading of various investors posing different impacts on
the return process. 2
▶ uninformed investors (noise traders) lead to higher serial correlations in
returns that make the volatility increase.
▶ informed investors suggest no autocorrelation.
1Black (1976), American Statistical Association Business and Economics Statistics Section.
2Avramov et al. (2006) The Review of Financial Studies 19, 1241.
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6. approaches for detecting asymmetric volatility effects
■ traditional approaches
Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-class models:
▶ TGARCH, EGARCH, JGR-GARCH, ST-GARCH etc..
▶ these models focus more on the linear correlations of returns and volatility
fluctuations without the nonlinear properties such as scaling properties.
▶ results for cryptocurrency markets seem rather mixed.
−→ asymmetric volatility or inverse-asymmetric volatility?
■ an alternative approach 3
use the asymmetric detrended cross-correlation coefficient (A-DCCA coefficient):
▶ a dynamical approach that accounts for nonlinearity and asymmetry.
▶ the method does not require the specification of a statistical model, and it is
easy to implement.
3Kakinaka and Umeno (2021), arXiv:2102.02865.
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7. Data: price change (return) and volatility change
▶ Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), Litecoin (LTC);
2016/6/1-2020/12/28 (https://poloniex.com/)
2017 2018 2019 2020 2021
0.4
0.2
0.0
0.2
r
t
2017 2018 2019 2020 2021
Date
1
0
1
2
v
t
(a) BTC
2017 2018 2019 2020 2021
0.6
0.4
0.2
0.0
0.2
r
t
2017 2018 2019 2020 2021
Date
1.5
1.0
0.5
0.0
0.5
1.0
1.5
v
t
(b) ETH
2017 2018 2019 2020 2021
0.5
0.0
0.5
1.0
r
t
2017 2018 2019 2020 2021
Date
7.5
5.0
2.5
0.0
2.5
5.0
7.5
v
t
(c) XRP
2017 2018 2019 2020 2021
0.4
0.2
0.0
0.2
0.4
0.6
r
t
2017 2018 2019 2020 2021
Date
2
1
0
1
2
v
t
(d) LTC
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8. Results: major cryptocurrencies [arXiv:2102.02865]
50 100 150 200 250 300
lags (scales)
1.00
0.75
0.50
0.25
0.00
0.25
0.50
0.75
1.00
DCCA
cross-correlation
coefficient
DCCA: overall
+
DCCA: uptrend
DCCA: downtrend
(a) BTC
50 100 150 200 250 300
lags (scales)
1.00
0.75
0.50
0.25
0.00
0.25
0.50
0.75
1.00
DCCA
cross-correlation
coefficient
DCCA: overall
+
DCCA: uptrend
DCCA: downtrend
(b) ETH
Figure: A-DCCA cross-correlation coefficients between the price-volatility relationships
under various lags (scales).
▶ stronger cross-correlations between price and volatility are present in bear
markets (downtrend) for Bitcoin and Ethereum.
−→ asymmetric volatility effect due to the dominance of noise traders
in bear markets.
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9. Results: minor cryptocurrencies [arXiv:2102.02865]
50 100 150 200 250 300
lags (scales)
1.00
0.75
0.50
0.25
0.00
0.25
0.50
0.75
1.00
DCCA
cross-correlation
coefficient
DCCA: overall
+
DCCA: uptrend
DCCA: downtrend
(a) XRP
50 100 150 200 250 300
lags (scales)
1.00
0.75
0.50
0.25
0.00
0.25
0.50
0.75
1.00
DCCA
cross-correlation
coefficient
DCCA: overall
+
DCCA: uptrend
DCCA: downtrend
(b) LTC
Figure: A-DCCA cross-correlation coefficients between the price-volatility relationships
under various lags (scales).
▶ stronger cross-correlations between price and volatility are present in bull
markets (uptrend) for Ripple and Litecoin.
−→ inverse-asymmetric volatility effect due to the dominance of
noise traders in bull markets.
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10. ■ Highlights:
▶ We examine the behavior in cryptocurrency price-volatility cross-correlations.
▶ The presence of asymmetric reactions in the volatility process to price
fluctuations between bull and bear regimes are confirmed.
▶ Stronger cross-correlations between price and volatility are present in bear
markets for major cryptocurrencies.
▶ Stronger cross-correlations between price and volatility are present in bull
markets for minor cryptocurrencies.
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11. Thank you
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