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

Jakub Ječmínek; Gabriela Kukalová; Lukáš Moravec

doi:10.2478/danb-2020-0015

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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

**Daily logarithmic returns**
*Source: Data from CoinMarketCap, own research*

**Histogram of Bitcoin, Ether and Ripple**
*Source: Data from CoinMarketCap, own research*

Table 1

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

[i] Source: Data from CoinMarketCap, own research

**Series with 2 Conditional SD Superimposed**
*Source: Data from CoinMarketCap, own research*

Table 2

Volatility and VaR forecast based on EWMA model

	${\hat{σ}}_{t}$	${\hat{σ}}_{t + 1}$	VaR_t+1	VaR_t+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

[i] Source: Data from CoinMarketCap, own research

Table 3

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***

[i] Note: Asterisks denote significance level at 10% (5% and 1% respectively)

[ii] Source: Data from CoinMarketCap, own research

Table 4

VaR computed using GARCH model

	${\hat{σ}}_{t + 1}$	VaR_t+1	VaR_t+10
Bitcoin	0.03340	$ 54.015	$ 175.33
Ether	0.04028	$ 66.314	$ 257.69
Ripple	0.03958	$ 68.740	$ 336.26

[i] Source: Data from CoinMarketCap, own research

Table 5

Historical VaR

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

[i] Source: Data from CoinMarketCap, own research

**Histogram with 95% VaR**
*Source: Data from CoinMarketCap, own research*

**One price path given by Geometric Brownian Motion**
*Source: Data from CoinMarketCap, own research*

**Thousands price paths given by Geometric Brownian Motion**
*Source: Data from CoinMarketCap, own research*

Table 6

Monte Carlo VaR

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

[i] Source: Data from CoinMarketCap, own research

References

Authors

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Articles in this issue

DOI: https://doi.org/10.2478/danb-2020-0015 | Journal eISSN: 1804-8285 | Journal ISSN: 1804-6746 (formerly 1804-8285)

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Language: English

Page range: 253 - 269

Published on: Oct 17, 2020

Published by: European Research University

In partnership with: Paradigm Publishing Services

Keywords:

Cryptocurrency,

Volatility,

Value-at-risk,

VaR,

Geometric Brownian Motion,

GARCH

Related subjects:

Business and economics,

Law,

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

Volume 11 (2020): Issue 3 (September 2020)

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

Figures & Tables

Figure 1

Figure 2

Table 1

Figure 3

Table 2

Table 3

Table 4

Table 5

Figure 4

Figure 5

Figure 6

Table 6

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