Volatility Spillover and Shock Transmission of Ethereum with Ripple, Stellar and Monero

Abstract

This study investigates the pairwise shock transmission and volatility spillover of Ethereum with Ripple, Stellar and Monero. The BEKK model has been deployed between 8 August 2015 and 30 September 2019. The results indicate a significant shock transmission from Ethereum to Ripple and Monero, but not on Stellar. On the other hand, shock transmission is only found from Ripple to Ethereum. Bi-directional volatility spillover was identified between Ethereum and both Ripple and Stellar. Uni-directional volatility spillover was present from Ethereum to Monero but not vice versa.

Full text

The Empirical Economics Letters, 19(4): (April 2020) ISSN 1681 8997
Volatility Spillover and Shock Transmission of Ethereum
with Ripple, Stellar and Monero
Vaibhav Aggarwal*
Department of Finance, Apeejay School of Management
Delhi, India
Email: efpm06004@iiml.ac.in
Adesh Doifode
Department of Finance, Pune Institute of Business Management
Pune, India
Email: equity.adesh@gmail.com
Abstract: This study investigates the pairwise shock transmission and volatility
spillover of Ethereum with Ripple, Stellar and Monero. The BEKK model has
been deployed between 8 August 2015 and 30 September 2019. The results
indicate a significant shock transmission from Ethereum to Ripple and Monero,
but not on Stellar. On the other hand, shock transmission is only found from
Ripple to Ethereum. Bi-directional volatility spillover was identified between
Ethereum and both Ripple and Stellar. Uni-directional volatility spillover was
present from Ethereum to Monero but not vice versa.
Keywords: Volatility spillover, BEKK-GARCH, Ethereum,Ripple, Stellar,
Monero
JEL Classification Number: C5, G1, G23
1. Introduction
Cryptocurrencies, over the past decade, have gained enormous traction with a total market
capitalisation of $256.07 billion as of September 2019 (CoinMarketCap, 2019). While the
Bitcoincontinues to remain the most popular with a market capitalisation of $171.2 billion
in September 2019, the emergence of new cryptocurrencies has also attracted a sizable
interest from media, academics, and investors. Subsequently, the share of Bitcoin has now
fallen to 68.0% of the overall cryptocurrency market capitalisation as compared to 89% in
2017.The leadership position of Bitcoin will be challenged further as the blockchain
technology matures in the future (Corbet, et.al., 2019). Ethereum is the second-largest
cryptocurrency and has seen its market capitalisation increased from a mere $0.07 billion
to $19.41 billion between December 2015 and September 2019, as depicted in Table 1.
* Corresponding Author: Email: efpm06004@iiml.ac.in

The Empirical Economics Letters, 19(4): (April 2020) 328
The market capitalisation of relatively smaller cryptocurrencies like Stellar and Monero
has also reached $1.23 billion and $0.97 billion respectively. The increase in market
capitalisation for all the cryptocurrencies has been accompanied by a substantial jump in
average daily trading volume, as seen in Table 1.
Table 1: Trading Volume and Market Capitalisation
Average Daily Volume (in Million)
Market Capitalisation (USD Million)
2015
2016
2017
2018
2019
31-Dec-
2015
31-Dec-
2016
31-Dec-
2017
31-Dec-
2018
30-Sep-
2019
Bitcoin
45.01
85.92
2382.87
6063.55
15387.23
6471.22
15492.55
237465.82
65331.50
149011.57
Ethereum
0.82
17.98
743.28
2276.87
6561.62
70.86
696.99
73170.17
13886.84
19419.15
Ripple
0.57
1.43
285.63
817.75
1196.49
202.58
234.33
89122.11
14388.35
11036.25
Stellar
0.01
0.09
30.30
106.93
234.90
8.47
17.09
6442.73
2161.59
1235.26
Monero
0.03
2.69
45.22
53.82
90.21
4.96
188.31
5426.21
771.41
979.26
Source: https://coinmarketcap.com/. Note: Volumes of 2015 and 2019 are included from the start
date and till the end date of the data taken for the study.
Cryptocurrencies have been an area of tremendous interest in academic research over the
past decade. Some researchers analyzed market efficiency in cryptocurrencies (Zhang,
et.al., 2018; Caporale, Gil-Alana, and Plastun, 2018; Tiwari, et.al., 2018). Recent strata of
research examined the diversification benefit of adding cryptocurrencies to an investment
portfoliothat has shown mixed results.(Akhtaruzzaman, Sensoy and Corbet, 2019; Corbet,
et.al., 2018; Bouri, et.al., 2017; Das, et.al., A.,2019).
But there is scant literature on shock transmission and volatility spillover among various
cryptocurrencies. Katsiampa, Corbet and Lucey (2019) found bi-directional shock
transmission and volatility spillover among Bitcoin and both Litecoin and Ethereum. They
further argued that there is volatility spillover from Ethereum to Litecoin. Fry and Cheah
(2016) found the presence of volatility spillover from Ripple to Bitcoin. Volatility
spillover from Bitcoin to Litecoin and Ethereum was found in a study for the period
between 2015 – 2018 (Kumar and Anandarao, 2019). Corbet, et.al. (2019) in their review
study emphasised the need for expanding the number of cryptocurrencies and the potential
diversification benefit in future studies which is a motivation for our research.
This paper contributes to this growing yet a thin body of research investigating whether
such interdependence among cryptocurrencies also extends to other newer ones like Stellar
and Monero which are seeing a substantial increase in trading volume and market cap.
The structure of the remaining paper is as follows. Section 2 depicts the data and its
preliminary analysis. Section 3 covers the methodology adopted. The results are discussed
in Section 4, and the conclusion is given in Section 5.

The Empirical Economics Letters, 19(4): (April 2020) 329
2. Data and Preliminary Analysis
The complete data of all the cryptocurrencies were collected from
www.coinmarketcap.com. All crypto assets used in this study are stated in Table 2. Daily
close prices were takenfrom 8 August 2015 to 30 September 2019 for calculating the daily
returns.
Table 2: Variable description
Name
Description
ETH
Ethereum Daily Closing Price Returns
XRP
Ripple Daily Closing Price Returns
XLM
Stellar Daily Closing Price Returns
XMR
Monero Daily Closing Price Returns
Non-normality was found at 1% significance level usingthe Jarque-Bera test. Stationarity
was validated using the Augmented Dickey-Fuller (ADF) (Dickey and Fuller, 1981) and
Philips and Perron (PP) (Philips and Perron, 1988) test statistics for all the data series.
Lastly, ARCH effect was also significant in all the data series.
Table 3: Descriptive Statistics
Period - 8 Aug 2015 to 30 Sept 2019
ETH
XRP
XLM
XMR
Mean
0.00508
0.00416
0.00454
0.00513
Maximum
0.41234
1.02736
0.72310
0.58464
Minimum
-1.30211
-0.61627
-0.36636
-0.29318
Standard Deviation
0.06818
0.06544
0.07343
0.06149
Skewness
-4.21296
3.65904
2.42697
1.26133
Kurtosis
95.40691
60.13020
25.09022
14.52691
Jarque-Bera
543508.3***
209411.7***
32290.88***
8789.11***
Observations
1515
1515
1515
1515
ARCH
5.302**
133.828***
256.762***
45.033***
Unit Root Tests
ADF
-6.3112***
-8.1259***
-11.5336***
-11.7314***
PP
-41.7435***
-40.8808***
-35.8071***
-40.5820***
Notes: ***, ** and * denotes the significance of the coefficient at 1%, 5% and 10% respectively.
ADF: Augmented Dickey-Fuller, PP: Phillips–Perron (unit root) tests for confirming stationarity.
Coefficients used for a unit root in the above model is mentioned using constant and linear trend.
ARCH Lagrange Multiplier test is applied for autoregressive conditional heteroscedasticity (ARCH)
using one lag.
A positive correlation is observed between all the cryptocurrencies, as shown in Table 4.
The strongest correlation is seen between XLM and XRP of 0.5367, followed by a
correlation between XLM and XMR of 0.354.

The Empirical Economics Letters, 19(4): (April 2020) 330
Table 4: Correlation Matrix
Period - 8 Aug 2015 to 30 Sept 2019
ETH
XRP
XLM
XMR
ETH
1.0000
XRP
0.1740
1.0000
XLM
0.2114
0.5367
1.0000
XMR
0.3125
0.2522
0.3549
1.0000
Note: Correlation coefficients among BTC, ETH, XRP, XLM and XMR
3. Methodology
BEKK-GARCH (Baba, Engle, Kraft and Kroner, 1990) methodology used to examine the
volatility impact between the selected crypto assets during the selected period. The
bivariate model is given below:
=(| 1) +  (1)
Var() = =′+11
′′+1′ (2)
In equation (1),  is 1
×
2 vector of ETH returns with XRP, XLM and XMR respectively.
While denotes the matrix of variance and covariance.
The variables J, K, L are used in the parameter matrix given as:
=11 0
21 22, =11 12
21 22, =11 12
21 22 (3)
In equation (3), L denotes triangular coefficient matrix whereas, matrices J and K are
squared coefficient. The BEKK–GARCH matrix is further elaborated below:
11 = ( 11
2 + 21
2) + (1 + 2)2 = ( 11
2 + 21
2) + (11
212 + 2111122 + 12
222) (4)
12 = (12 22 ) + (111+ 12 2) (211+ 222) = (12 22 ) + (112112)
+ (1121 +1122)12 + (1122 22) (5)
22 = (22
2) + (211 + 222)2 = (22
2) + 21
212 + 2211222 + 22
222 (6)
For 11, , the GARCH terms ignored is 11
211, 1+ 11 21 (21, 1 + 12, 1)
+ 12
222, 1;
For 12, , the GARCH terms ignored is 11 21 11,1 + (1221 + 11 22)12 , 1
+ 1222 22 , 1;
For 22, , the GARCH terms ignored is 21
211, 1+ 21 22 (21 , 1 + 12, 1)
+ 22
222, 1;

The Empirical Economics Letters, 19(4): (April 2020) 331
In equation (3), the variable ―J‖ represents the ARCH effect in the model, where j11
implies the impact on ETH of its own lagged value, j22 measures the impact on XRP,
XLM, and XMRof its own lagged values. j12 coefficient shows the shock transmission
from ETH to XRP, XLM and XMR; j21 estimates the shock transmission from XRP, XLM
and XMR to ETH. Likewise, the variable ―K‖ represents the GARCH effect, where k11
indicates the impact on current conditional volatility on ETH from its own past volatility,
k22 measures impact on current conditional volatility onXRP, XLM and XMRfrom own
past volatility. k12 represents the volatility spillover ETH to XRP, XLM and XMR; k21
measures the volatility spillover from XRP, XLM and XMR to ETH. The BFGS
(Broyden, Fletcher, Goldfarb, and Shanno) method is used for maximum likelihood
estimation in the BEKK-GARCH model, which is given as follows:
L(∂) = -T ln(2π) – 0.5 (

1|| + ′1) (7)
4. Results and Discussion
The estimation result of the relationship between crypto-assets is specified using the
BEKK-GARCH technique, as displayed in Table 5. To examine the interlinkages, and to
substantiate the use of the GARCH technique; initially, the ARCH effect was tested to be
significant in all the variables, as given in Table 3.
Table 5: Bivariate BEKK GARCH (1,1) Estimation
Period - 8 Aug 2015 to 30 Sept 2019
ETH - XRP
ETH - XLM
ETH - XMR
Variance Equation
L11
0.0000025
0.0000099**
0.0000018
L21
0.0000024
0.0000091*
-0.000007
L22
0.0000000
0.0000000
0.0000000
J11
0.4882000***
0.8101000***
0.7166000***
J12
0.1717000***
0.0152000
-0.0112000*
J21
0.1053000***
0.0034748
0.0178000
J22
0.4620000***
0.8147000***
0.5988000***
K11
0.9062000***
0.8305000***
0.8512000***
K12
-0.0585000***
-0.0175000***
0.0122000***
K21
-0.0389000***
-0.0164000***
-0.0119000
K22
0.9116000***
0.8259000***
0.8876000***
Model Diagnostics
AIC
-11.3410
-11.3710
-11.3830
Log-Likelihood
8604.0144
8626.9068000
8635.3735
Note: AIC refers to the Akaike Information Criterion. ***, ** and * denotes the significance of the
coefficient at 1%, 5% and 10% respectively.

The Empirical Economics Letters, 19(4): (April 2020) 332
There is bi-directional significant positive shock transmission between Ethereum and
Ripple, which is as seen from coefficients J12 and J21 respectively in Table 5. This implies
that the past news in Ethereum and Ripple is having a positive impact on the current
conditional volatility of Ripple and Ethereum, respectively. On the other hand, there is a
bi-directional negative volatility spillover between Ethereum and Ripple as depicted in K12
and K21, respectively. Consequently, the past volatility in Ethereum and Ripple is having a
negative spillover on the current conditional volatility of Ripple and Ethereum,
respectively.
No significant shock transmission is found between Ethereum and Stellar as seen in the
coefficients of J12 and J21. Whereas,significant bi-directional negative volatility spillover is
found between Ethereum and Stellaras depicted by coefficients K12 and K21, respectively.
Uni-directional negative shock transmission at 10% level of significance is observed from
Ethereum to Monero as shown by J12 coefficient in Table 5. However, no shock
transmission is detected from Monero to Ethereum, as seen in the coefficient of J21. On
similar lines, only significant volatility spillover from Ethereum to Monero is found as
depicted in coefficient K12.
5. Conclusion
This study, using the BEKK-GARCH methodology, has analysed the pairwise conditional
volatility dynamics of Ethereum with Ripple, Stellar and Monero, respectively. The
findings suggest that there is bi-directional significant positive shock transmission
between Ethereum and Ripple and uni-directional shock transmission from Ethereum to
Monero. There is significant volatility spillover from Ethereum on the current conditional
volatility of all the other three cryptocurrencies, namely - Ripple, Stellar and Monero.
Also, there is a significant volatility spillover from Ripple and Stellar on Ethereum. The
only exception is Monero which did not have any significant volatility spillover on
Ethereum. These findings give further supporting evidence on the interlinkages between
various cryptocurrencies which can be useful for various investors and market players.
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