High frequency volatility co-movements in cryptocurrency markets
Paraskevi Katsiampa
a
, Shaen Corbet
b∗
, Brian Lucey
c,d,e
a
Sheffield University Management School, The University of Sheffield, Conduit road, Sheffield, S10 1FL,
UK
b
DCU Business School, Dublin City University, Dublin 9
c
Trinity Business School, Trinity College Dublin, Dublin 2
d
University of Sydney Business School, H70, Abercrombie St & Codrington St, Darlington NSW 2006,
Australia
e
Institute of Business Research, University of Economics Ho Chi Minh City, 59C Nguyen Dinh Chieu,
Ward 6, District 3, Ho Chi Minh City, Vietnam
Abstract
Through the application of Diagonal BEKK and Asymmetric Diagonal BEKK method-
ologies to intra-day data for eight cryptocurrencies, this paper investigates not only condi-
tional volatility dynamics of major cryptocurrencies, but also their volatility co-movements.
We first provide evidence that all conditional variances are significantly affected by both
previous squared errors and past conditional volatility. It is also shown that both method-
ologies indicate that cryptocurrency investors pay the most attention to news relating to
Neo and the least attention to news relating to Dash, while shocks in OmiseGo persist the
least and shocks in Bitcoin persist the most, although all of the considered cryptocurren-
cies possess high levels of persistence of volatility over time. We also demonstrate that the
conditional covariances are significantly affected by both cross-products of past error terms
and past conditional covariances, suggesting strong interdependencies between cryptocur-
rencies. It is also demonstrated that the Asymmetric Diagonal BEKK model is a superior
choice of methodology, with our results suggesting significant asymmetric effects of positive
and negative shocks in the conditional volatility of the price returns of all of our investigated
cryptocurrencies, while the conditional covariances capture asymmetric effects of good and
bad news accordingly. Finally, it is shown that time-varying conditional correlations exist,
with our selected cryptocurrencies being strongly positively correlated, further highlighting
interdependencies within cryptocurrency markets.
Keywords: Cryptocurrencies; High-frequency data; Asymmetric Diagonal BEKK;
MGARCH; Volatility.
Preprint submitted to SSRN August 4, 2020
1. Introduction
As cryptocurrency markets and exchanges continue to evolve, it is vital to further de-
velop our understanding as to the way in which these markets operate. One avenue of par-
ticular interest is based on the conditional volatility dynamics along with the interlinkages
and conditional correlations between the largest international cryptocurrencies. Through
an investigation of these market interlinkages, we can help to answer key questions which
have been asked of not only the integrity of cryptocurrency markets, but indeed, questions
based on time-varying effects and the underlying fundamentals of these new exchanges
and financial market products. Regulatory bodies and policy-makers alike have observed
the growth of cryptocurrencies with a certain amount of scepticism based on the growing
potential for illegality and malpractice through the use of cryptocurrencies
1
.
While cryptocurrency price dynamics have been extensively studied in the literature,
the potential for market manipulation appears to have been broadly identified in cryp-
tocurrency cross-correlations and market interdependencies (Katsiampa et al. [2019]). For
instance, Griffins and Shams [2018] examined whether Tether influenced Bitcoin and other
cryptocurrency prices to find that purchases with Tether were timed following market down-
turns and resulted in significant increases in the price of Bitcoin. Further, less than 1% of
the hours in which Tether experienced significant transactions were found to be associated
with 50% of the increase of Bitcoin prices and 64% of other top cryptocurrencies, draw-
ing the damning conclusion that Tether was used to provide price support and manipulate
cryptocurrency prices. Furthermore, Gandal et al. [2018] identified the impact of suspicious
trading activity on the Mt.Gox Bitcoin exchange theft when approximately 600,000 Bit-
coins were attained. The authors demonstrated that the suspicious trading likely caused the
spike in price in late 2013 from $150 to $1,000, most likely driven by one single actor. These
two significant pieces of research have fine-tuned the focus of regulators, policy-makers and
academics alike, as the future growth of cryptocurrencies cannot be sustained at pace with
such significant questions of abnormality remaining unanswered. To develop on this we
must focus on interdependencies within cryptocurrency markets, which continue to remain
relatively under-explored. Despite the fact that the interconnectedness of cryptocurren-
cies has been studied by, e.g., Fry and Cheah [2016], Ciaian et al. [2018], Corbet et al.
[2018], Katsiampa [2017], Katsiampa et al. [2019], and Koutmos [2018], all of whom em-
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Some many regulatory authorities such as the International Monetary Fund (IMF) have expressed their
satisfaction with the product’s development and the benefits that are contained within its continued growth
(An Even-handed Approach to Cryptocurrencies, IMF blogpost written by Christine Lagarde, Head of the
International Monetary Fund, available at: https://blogs.imf.org/2018/04/16/an-even-handed-approach-
to-crypto-assets/), the Securities and Exchange Commission (SEC) in 2018 have backtracked on earlier
positivity to warn of the inherent potential for spoofing and other market manipulation techniques (US
Securities and Exchange Commission, Public Statement, Statement on Potentially Unlawful Online Plat-
forms for Trading Digital Assets, Available at: https://www.sec.gov/news/public-statement/enforcement-
tm-statement-potentially-unlawful-online-platforms-trading)
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ployed daily data, there has been limited research conducted on volatility interdependencies
within cryptocurrency markets - especially while allowing for asymmetric effects of positive
and negative shocks in cryptocurrencies’ volatility dynamics - although volatility modelling
is important for many option pricing, portfolio selection, and risk management applications
(Fleming et al. [2003]), while understanding covariances and correlations is important for
determining the risk of an investor’s portfolio (Coudert et al. [2015]). What is more, to the
best of the authors’ knowledge, no previous study has examined interdependencies within
cryptocurrency markets using high-frequency data, which can provide cryptocurrency users
and investors with better insights into market behaviours and dynamics.
Consequently, using intraday data for eight cryptocurrencies, namely Bitcoin, Ethereum,
Litecoin, Dash, Ethereum Classic, Monero, Neo, and OmiseGO, in this study we utilise the
Diagonal BEKK-MGARCH and Asymmetric Diagonal BEKK-MGARCH models which can
be used to examine volatility co-movements. The Diagonal BEKK methodology itself is
similar to the BEKK model of Engle and Kroner [1995]. However, in the Diagonal BEKK
model the number of parameters to be estimated is considerably reduced, while guarantee-
ing the positive definiteness of the conditional covariance matrix (Terrell and Fomby [2006]).
On the other hand, the Asymmetric Diagonal BEKK methodology allows for asymmetric
responses of positive and negative shocks to the cryptocurrencies’ conditional volatility
and covariances, while still guaranteeing the positive definiteness of the conditional covari-
ance matrix (Katsiampa [2018]). It is shown that our selected cryptocurrencies’ pairwise
price returns are strongly positively correlated and all conditional variances are significantly
affected by both previous squared errors and past conditional volatility. Both the Diago-
nal BEKK and Asymmetric Diagonal BEKK methodologies indicate that cryptocurrency
investors pay the most attention to news relating to Neo and the least attention to news
relating to Dash, while, although all investigated cryptocurrencies possess high levels of per-
sistence of volatility over time, shocks in OmiseGo persist the least and shocks in Bitcoin
persist the most. Furthermore, we find evidence that all estimates of asymmetry are pos-
itive and statistically significant, indicating significant asymmetric effects of both positive
and negative shocks in the conditional volatility of the price returns of all of our investi-
gated cryptocurrencies. The conditional covariances are found to be significantly affected
by cross products of past error terms and past conditional covariances using both method-
ologies, which is indicative of strong interdependencies between cryptocurrencies, while the
significant estimates for the asymmetry terms indicate that the conditional covariances also
capture asymmetric effects of both good and bad news accordingly.
The structure of the remainder of the paper is as follows: Section 2 investigates related
previous literature. Section 3 describes the data and Multivariate GARCH methodology
employed. The empirical findings are discussed in section 4. Finally, some concluding
remarks are given in section 5.
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2. Previous Literature
Multivariate GARCH models have been used throughout a host of financial market-
based research in recent years. For instance, Choudhry and Wu [2008] investigated the
forecasting ability of GARCH methodologies inclusive of BEKK-GARCH, in comparison to
the Kalman filter methodology on UK time-varying beta’s, while Trujillo-Barrera et al.
[2012] considered the same methodology when investigating volatility spillovers in the
United States from crude oil futures prices to find that the share of corn and ethanol price
variability directly attributed to volatility in the crude oil market was generally between
10% and 20%, but reached almost 45% during the international financial crisis. Moreover,
Chng [2009] investigated the cross-market trading dynamics in futures contracts on the
Tokyo Commodity Exchange using a BEKK-GARCH methodology to find that natural
rubber, palladium and gasoline futures are driven in principal by a common industry which
is found to be the automobile industry, while Mensi et al. [2014] used the VAR-BEKK-
GARCH methodology on the daily spot prices of eight international commodity markets to
provide evidence of significant links between energy and cereal markets, with OPEC new
announcements being found to exert influence on oil markets and the oil and cereal rela-
tionship. Research of such nature can be used to improve the risk-adjusted performance by
having more diversified portfolios to hedge risk more effectively. Haixia and Shiping [2013]
identified evidence of uni-directional spillover effects from crude oil markets to corn and fuel
ethanol markets when analysing commodity markets in China using a BEKK-MGARCH
model with further evidence of double-directional spillovers between corn and fuel ethanol,
while in another Chinese-based study, Arouri et al. [2015] studied the hedging and diver-
sification effectiveness of gold and stocks in China to find evidence of significant return
and volatility cross-effects, while gold acted as a hedge for stocks and a safe haven during
financial crisis. Using BEKK, DCC, DECO and ADCC-GARCH methodologies, Mimouni
et al. [2016] explored diversification benefits in developed, emerging, GCC and global port-
folio stock markets to find that correlations and diversification benefits are time-varying
and that such trends and correlations reversed in 2012. Another interesting use of the
BEKK-MGARCH methodology was that in the study of Bekiros [2014] who investigated
the influence of the US financial crisis on BRIC markets to find that BRICs are integrated,
contagion is substantiated and there is little evidence of decoupling using an MGARCH
methodology. On the other hand, the use of the Diagonal BEKK-GARCH methodology
has been used in research such as that of Bai and Koong [2018] who investigated the time-
varying trilateral relationships between oil prices, exchange rate changes and stock market
returns in China and the US between 1991 and 2015. Moreover, Boldanov et al. [2016]
investigated the dynamic correlation between oil prices and stock markets for six major
oil-importing and oil-exporting countries between 2000 and 2014 to find heterogeneous pat-
terns and strong correlations to major economic and geopolitical events using a Diagonal
BEKK model. Using a similar methodology Basher et al. [2012] studied the relationship
between oil prices, exchange rates and emerging stock markets and Degiannakis and Floros
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[2010] investigated hedge ratios in South African stock index futures.
Other than financial and commodity markets, recently there has been an increased in-
terest in studying the price volatility of cryptocurrencies as well as the interconnectedness
between cryptocurrencies and various economic and financial assets. While investigating
the general behavioural aspects of cryptocurrencies, Corbet et al. [2018] examined the re-
action of a broad set of digital assets to US Federal Fund interest rates and quantitative
easing announcements to find a broad range of differing volatility responses dependent on
the type of cryptocurrency investigated and as to whether the cryptocurrency was mine-
able or not. Other studies of the volatility of cryptocurrency price returns include those
of Corbet et al. [2019], Chu et al. [2017], Katsiampa [2017], Baur and Dimpfl [2018] and
Phillip et al. [2018], among others, which have employed a broad range of volatility mod-
els in order to examine the volatility behaviour of cryptocurrencies. On the other hand,
examples of studies on the interconnectedness between cryptocurrencies and other assets
include, e.g., those of Bouri et al. [2017], Corbet et al. [2018], Giudici and Abu-Hashish
[2018], Guesmi et al. [2018], Ji et al. [2018], and Chuen et al. [2018], the findings of which
suggest that cryptocurrencies are isolated from other markets. More specifically, using a
dynamic conditional correlation model, Chuen et al. [2018] studied co-movements between
the Cryptocurrency Index (CRIX) and mainstream assets, such as SP 500, T-Note, Gold,
Oil and REITs, and concluded that the return correlations between cryptocurrencies and
other assets are low, while Bouri et al. [2017] examined as to whether Bitcoin could act
as a hedge and safe haven for four major world stock indices, bond, oil, gold, the general
commodity index and the US dollar index finding that it is a poor hedge and is suitable for
diversification purposes only. Moreover, Corbet et al. [2019] found evidence of the relative
isolation of cryptocurrencies from financial and economic assets and that cryptocurrencies
may offer diversification benefits for investors with short investment horizons, and Guesmi
et al. [2018] analysed the conditional cross effects and volatility spillovers between Bitcoin
and other financial assets providing further evidence that Bitcoin can offer diversification
benefits and hedging opportunities for investors, while finding that hedging strategies in-
volving gold, oil, emerging stock markets and Bitcoin reduce considerably a portfolio’s
variance in comparison to the variance of a portfolio composed of gold, oil and stocks from
emerging stock only. The relationships between Bitcoin and other assets have been also
analysed by Ji et al. [2018], who employed a data-driven methodology, the so-called direct
acyclic graph, applied to daily index values for Bitcoin, stock, bonds, commodities and cur-
rencies and found that Bitcoin is isolated from other assets, none of which can significantly
influence the Bitcoin market, as well as by Giudici and Abu-Hashish [2018], who developed
an extended Vector Autoregressive model based on network models that introduce a con-
temporaneous contagion component that describes contagion effects between asset prices
and also concluded that correlation of Bitcoin prices with traditional assets is low. In con-
trast, Urquhart and Zhang [2018] assessed the relationship between Bitcoin and currencies
at the hourly frequency and found that Bitcoin can be an intraday hedge for the CHF, EUR
and GBP, but acts as a diversifier for the AUD, CAD and JPY. The authors also found
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