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

Jakub Ječmínek
Jakub Ječmínek
, 
Gabriela Kukalová
Gabriela Kukalová
 e 
Lukáš Moravec
Lukáš Moravec
   | 17 ott 2020
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INFORMAZIONI SU QUESTO ARTICOLO
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Pubblicato online: 17 ott 2020
Pagine: 253 - 269
DOI: https://doi.org/10.2478/danb-2020-0015
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© 2020 Jakub Ječmínek et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Bitcoin Ether Ripple
Minimum −0.266198 −1.302106 −0.616273
Maximum 0.357451 0.412337 1.027356
1st Quartile −0.012615 −0.024548 −0.022698
3rd Quartile 0.018402 0.0284860 0.020083
Mean 0.001750 0.002700 0.001679
Median 0.001883 −0.000802 −0.002762
Sum 4.178293 4.204154 3.845187
Variance 0.001848 0.005229 0.005384
Stdev 0.042991 0.072313 0.073372
Skewness −0.162197 −3.412472 2.057162
Kurtosis 7.637610 70.186393 29.374596

VaR computed using GARCH model

σ^t+1 {\hat \sigma _{t + 1}} VaRt+1 VaRt+10
Bitcoin 0.03340 $ 54.015 $ 175.33
Ether 0.04028 $ 66.314 $ 257.69
Ripple 0.03958 $ 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+1 VaRt+10
Bitcoin 0.03351 0.03358 $ 55.41 $ 175.21
Ether 0.02972 0.02925 $ 48.26 $ 152.62
Ripple 0.03503 0.03489 $ 57.57 $ 182.05

Optimal parameters based on standard GARCH modelling

mu alpha0 alpha1 beta1
Bitcoin 0.001095* 0.000073*** 0.143602*** 0.824987***
Ether 0.000148 0.000407*** 0.194669*** 0.704177***
Ripple −0.003432*** 0.000417*** 0.397415*** 0.594709***

Historical VaR

Digital asset Historical VaR
Bitcoin $ 66.16
Ether $ 92.81
Ripple $ 91.88

Monte Carlo VaR

VaRt+1 VaRt+10
Bitcoin $ 124.079 $ 342.515
Ether $ 88.355 $ 291.802
Ripple $ 160.696 $ 490.118
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