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Volatility Modelling and VaR: The Case of Bitcoin, Ether and Ripple Cover

Volatility Modelling and VaR: The Case of Bitcoin, Ether and Ripple

DANUBE
Volume 11 (2020): Issue 3 (September 2020)
By: Jakub Ječmínek,  Gabriela Kukalová and  Lukáš Moravec  
Open Access
|Oct 2020

Figures & Tables

Figure 1

Daily logarithmic returnsSource: Data from CoinMarketCap, own research
Daily logarithmic returnsSource: Data from CoinMarketCap, own research

Figure 2

Histogram of Bitcoin, Ether and RippleSource: Data from CoinMarketCap, own research
Histogram of Bitcoin, Ether and RippleSource: Data from CoinMarketCap, own research

Figure 3

Series with 2 Conditional SD SuperimposedSource: Data from CoinMarketCap, own research
Series with 2 Conditional SD SuperimposedSource: Data from CoinMarketCap, own research

Figure 4

Histogram with 95% VaRSource: Data from CoinMarketCap, own research
Histogram with 95% VaRSource: Data from CoinMarketCap, own research

Figure 5

One price path given by Geometric Brownian MotionSource: Data from CoinMarketCap, own research
One price path given by Geometric Brownian MotionSource: Data from CoinMarketCap, own research

Figure 6

Thousands price paths given by Geometric Brownian MotionSource: Data from CoinMarketCap, own research
Thousands price paths given by Geometric Brownian MotionSource: Data from CoinMarketCap, own research

Basic statistics

BitcoinEtherRipple
Minimum−0.266198−1.302106−0.616273
Maximum0.3574510.4123371.027356
1st Quartile−0.012615−0.024548−0.022698
3rd Quartile0.0184020.02848600.020083
Mean0.0017500.0027000.001679
Median0.001883−0.000802−0.002762
Sum4.1782934.2041543.845187
Variance0.0018480.0052290.005384
Stdev0.0429910.0723130.073372
Skewness−0.162197−3.4124722.057162
Kurtosis7.63761070.18639329.374596

VaR computed using GARCH model

σ^t+1 {\hat \sigma _{t + 1}} VaRt+1VaRt+10
Bitcoin0.03340$ 54.015$ 175.33
Ether0.04028$ 66.314$ 257.69
Ripple0.03958$ 68.740$ 336.26

Volatility and VaR forecast based on EWMA model

σ^t {\hat \sigma _t} σ^t+1 {\hat \sigma _{t + 1}} VaRt+1VaRt+10
Bitcoin0.033510.03358$ 55.41$ 175.21
Ether0.029720.02925$ 48.26$ 152.62
Ripple0.035030.03489$ 57.57$ 182.05

Optimal parameters based on standard GARCH modelling

mualpha0alpha1beta1
Bitcoin0.001095*0.000073***0.143602***0.824987***
Ether0.0001480.000407***0.194669***0.704177***
Ripple−0.003432***0.000417***0.397415***0.594709***

Historical VaR

Digital assetHistorical VaR
Bitcoin$ 66.16
Ether$ 92.81
Ripple$ 91.88

Monte Carlo VaR

VaRt+1VaRt+10
Bitcoin$ 124.079$ 342.515
Ether$ 88.355$ 291.802
Ripple$ 160.696$ 490.118
DOI: https://doi.org/10.2478/danb-2020-0015 | Journal eISSN: 1804-8285 | Journal ISSN: 1804-6746
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Language: English
Page range: 253 - 269
Published on: Oct 17, 2020
Published by: European Association Comenius - EACO
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
Cryptocurrency,
Volatility,
Value-at-risk,
VaR,
Geometric Brownian Motion,
GARCH
Related subjects:
Business and economics,
Political economics,
Macroeconomics,
Economic policy,
Law,
European law,
European law, other,
Law, other

© 2020 Jakub Ječmínek, Gabriela Kukalová, Lukáš Moravec, published by European Association Comenius - EACO
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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