Jéssica Gonçalves Andrade
Universidade Federal Fluminense (UFF), Brazil
E-mail: jessiica_andrade@hotmail.com
Nilson Brandalise
Universidade Federal Fluminense (UFF), Brazil
E-mail: nilson_01@yahoo.com.br
Submission: 23/07/2018
Accept: 09/08/2018
ABSTRACT
In order to do a
volatility analysis, since the exchange rate is higher than the average risk,
the higher the average rate of return, the higher the average growth rate of
the year. applied the method of data analysis. An attempt to volatility
analysis can be made in one year, in the middle of the end of 2016.
Keywords: Virtual
Currencies; Volatility; Garch Model
1. INTRODUCTION
International
financial institutions have reduced the money needs of the bankless poor to
their supposed need for money from banks, while mobile network operators,
international payment providers, and academic researchers have speculatively
placed them in relation to digital money or mobile money (CHIPERE, 2018).
Currently
there is a huge variety of virtual currencies in the financial market, while
the most well-known and cited is Bitcoin,
for being the pioneer. The general objective of this article is to make a
volatility analysis of the virtual currencies Bitcoin and Ethereum,
because they are considered of greater impact in the economy. It is known that
institutional volatility would therefore be a better systemic risk metric than
discrete news or policy changes (HARTWELL, 2018).
In
order to study the volatility, the Garch method was used as a tool for risk
analysis. We can see a rapid and drastic change produced by the new
technologies in man's relations with money, as well as the new configurations
that are established with the virtualization.
A
correlation analysis was performed between the Bitcoins and Ethereum currencies
because an investor needs to be aware in order to price this part of the
financial risk (BARUNIK; VACHA, 2018).
The
article is divided into chapters, the first being the introduction regarding
the presentation of the problem, the general objective, as well as its
justifications. Second chapter deals with the bibliographic survey on
crypto-coins, GARCH method, correlation and volatility. The third chapter
demonstrates the methodology used in the research. The fourth chapter deals
with data collection. Fifth chapter is demonstrated the data analysis, finally
the conclusions observed and the bibliographical references.
2. BIBLIOGRAPHIC BASE
2.1.
Local
Currencies
They
are based on the logic of encouraging circulation in a very small group of
people as a way to promote economic development, using, for this, physical
instruments identified and used as currency
(FOBE, 2016).
By
investing in local currency denominated securities, foreign investors increase
the diversification of their financial portfolios and gain exposure to rapidly
growing economies (BORRI, 2017).
The
emergence of local currencies articulate concrete instruments that allow the
purchase and payment of debts, as well as acting as a "system of debt
settlement that translates to the existence of a system of payments", and
for assuming, in a systematic logic, also an institutional character (FOBE, 2016).
2.2.
Digital
Coins
The
21st century can be characterized with a vast development of technologies and
with the increase of the use of the internet that has significantly succeeded
the development of the monetary system introducing a new phenomenon - the
virtual currencies (DIBROVA, 2016).
From
the government's point of view, a digital private currency can be considered a
foreign currency because the central bank cannot control its supply as opposed
to conventional fiduciary money (issued by the government) (RAHMAN, 2018).
Digital
coins offer the possibility of substantially reducing transaction fees for
online purchases. These payment platforms are so dominant that they can charge
high fees despite the low operating costs. Supporters of the new digital
currencies believe they can offer lower transaction fees through technological
innovation than regulation. Of course, it remains to be seen whether they can
overtake Visa and MasterCard's entrenched payment networks (MOORE, 2013).
Digital
currencies, in turn, have the following advantages: (i) instant transactions,
(ii) low or no cost, and (iii) without territorial borders. Digital currencies,
therefore, are those used by a community of users that seeks, in addition to
the advantages mentioned above, the support offered by the internet as the
basis for their transactions. No internet, no need to talk about digital
currency (FOBE, 2016).
2.3.
Bitcoin
and Ethereum
Bitcoin
has become one of the most popular and volatile assets on the market in just
nine years since it came into operation in 2009. Despite its notable
speculative component (BAEK; ELBECK, 2015) and with a fundamental value equal
to zero (CHEAH; FRY, 2015), this criptomoeda has attracted the attention of
many companies and academics of different areas. In particular, the research on
Bitcoin was based primarily on computational aspects, given its innovative
technology (SWAN, 2015; VIDAL-TOMÁSA, 2018).
Bitcoin is a revolution in
remittances, remittances could not be simpler. exorbitant fees for sending
money, but seriously threatens financial intermediation as we know it, since it
is no longer possible simply to create money, but also makes the future
financial crisis impossible (KUBÁT, 2015).
Ethereum is an Open Source platform
focused on the creation and distribution of decentralized applications.
Applications that do not need intermediaries, can interact with social systems,
financial systems, game interface and anything else < https://portaldobitcoin.com/tudo-sobre-ethereum/>.
2.4.
Currency
volatility
Volatility plays an important role
in risk modeling and assessment, as well as in the pricing of complex financial
products. Therefore, studying the inherent characteristics of the conditional
variance of financial time series has received a growing interest in economics
recently (LAHMIRI; BEKIROS; SALVI, 2018).
Since the first transactions of
2009, Bitcoin had a relatively stable up until 2011, when prices fluctuated
strongly between the cycles of appreciation and depreciation, Bitcoin's value
grew rapidly from US $ 0.30 to US $ 32, after which it fell to $ 2. By the end
of 2012, Bitcoin was trading nearly $ 13 before being widely accepted and
speculators to raise prices (GEORGETA, 2016).
As Bitcoin is used primarily as an
asset rather than a currency (BITTENBERG et al., 2004), the Bitcoin market is
currently highly speculative and more volatile and susceptible to speculative
bubbles. than other currencies (GRINBERG, 2011; CHEAH; FRY, 2015). Bitcoin
therefore has a place in financial markets and portfolio management (DYHRBERG,
2016a), and to examine its volatility is crucial (KATSIAMPA, 2017).
Thus, during the Cypriot financial
crisis, the price of Bitcoin rose, peaking at $ 266 on April 10, 2013, then
falling to $ 50 / Bitcoin (GEORGETA, 2016).
2.5.
Garch
Method
The ideal model of conditional
heteroscedasticity is explored with respect to the adequacy of Bitcoin's price
data. It is verified that the best model is the AR-CGARCH model, highlighting
the importance of including a short- and long-term component of the conditional
variance (KATSIAMPA, 2017).
Few would argue that Engle's
autoregressive conditional heteroscedasticity (ARCH) model and Bollerslev's
generalized ARCH (GARCH) model, along with its various extensions, are
excellent tools for modeling and predicting the dynamic characteristics of
condition volatility. . Conventional GARCH models, which use the daily closing
price to infer conditional volatility, may omit certain useful intraday
information (JIANG et al., 2018).
For statistical inference in GARCH
models, numerous studies have been carried out. A GARCH model (1, 1) is defined
as:
yt = ŋt √ht,
t= 1, 2... |
(1) |
|
(2) |
com valores iniciais y0 e h0 ≥ 0,
onde: w > 0, α e β ≥ 0, e { ŋt : t ≥ 0 }.
The GARCH model
(1, 1) is now tremendously successful in empirical work on econometrics and
finance and is regarded as the benchmark model for capturing conditional
volatilities by many economists (DONG; MUYI; WUQING, 2014).
Let η be a generic
random variable with the same distribution as ηt. The largest Lyapunov exponent
associated with the model (1.1) is given by:
γ=
Elog ( β + αŋ2 ) |
(3) |
The γ signal plays
a key role in the study model (1.1). It is well known that the necessary and
sufficient condition for the existence of a strict stationary solution for the
model (1.1) is γ ˂ 0 (DONG; MUYI; WUQING, 2014).
3. METHODOLOGY
The
method used to obtain the volatility results of the Bitcoin and Ethereum coins
was Garch (defined in section 2.5).
The
data were obtained from the virtual magazine yahho.com.br where it is updated
daily according to the behavior of the financial market. The data period was
from June / 2016 to June / 2018, and the collection was done in June / 2018.
The
tool for data analysis was Microsoft Office Excel, whose parameters used for
analysis were date and adjusted closure.
The
Garch parameters were then calculated as shown in Tables 1 and 2.
The
parameters of tables 1 and 2 made it possible to calculate the volatility of
the aforementioned currencies.
The
return series was calculated with the following calculation basis:
the conditional expectation of the
quadratic variation (VQt) is equal to the conditional variance of the returns,
Et-1
(VQt ) = Vart-1 (rt ) σt
2 |
(4) |
If VR is a non-skewed estimator of
quadratic variation, it follows that the conditional variance of returns can be
bound to VR as σt 2 = Et-1 (VRt), where the information combination is defined
as tt-1 {rt- 1, VRt-1, rt-2, VRt-2, ..., r1, VR1}. Assuming that the RV has
log-normal distribution, the restriction assumes the following form: (VAL; PINTO; KLOTZLE, 2014).
σ2 t
= Et-1 (VRt ) = exp (Et-1 log(VRt ) + Vart-1(log(VRt )) |
(5) |
4. SURVEY OF DATA
Figures
1 and 2 show the historical data of the Bitcoin and Ethereum currencies
respectively, relating the rate against the period.
Figure 1: Bitcoin currency tax
Source: Prepared by the authors
(2018).
Figure 2: Ethereum currency tax
Source: Prepared by the authors
(2018).
Figures
3 and 4 represent the return graphs of the Bitcoins and Ethereum coins
respectively.
Figure 3: Bitcoin Return Chart
Source: Prepared by the authors
(2018).
Figure 4: Ethereum Return Chart
Source: Prepared by the authors
(2018).
The reason for using series of
returns has two factors, the information of returns serve the interests of
investors and the series of returns has statistical properties more interesting
than series of prices (JIANG et al., 2018).
5. DATA ANALYSIS
Knowing that:
Uncond.
Var is the conditional variance in
period t;
α is the reaction coefficient of volatility;
β is the persistence coefficient of volatility;
Table 1: Parameters Garch Bitcoin
GARCH
Parameters Bitcoin |
|
Uncond.
Var |
136020,6636 |
ω
= |
11,86435603 |
α
= |
0,192052002 |
β
= |
0,807947998 |
persistence= |
1 |
Source: Prepared by the authors
(2018).
The Garch test that allowed us to
analyze the volatility of the Bitcoin currency showed that the series is not
conditional and had a persistence result of 1.
Table 2: Parameters Garch Ethereum
GARCH
Parameters Ethereum |
|
Uncond.
Var |
777,6144911 |
ω
= |
0,014229372 |
α
= |
0,241488738 |
β
= |
0,758511262 |
persistence= |
1 |
Source: Prepared by the authors (2018).
The
Garch test allowed to analyze currency volatility Ethereum showed that the
series is not conditional and had a persistence result of 1.
A
volatility analysis of the Bitcoin and Ethereum currencies was carried out as
shown in figures 5 and 6 because it is known that its correct estimation
assumes great relevance in risk and asset sizing and pricing, as well as in the
elaboration of investment strategies (PINHO;, 2016).
Figure 5: Graph of Volatility of the Bitcoin currency
Source: Prepared by the authors
(2018).
Figure 6: Graph of Volatility of the Ethereum currency
Source: Prepared by the authors
(2018).
Figure
5 shows that Bitcoin began to show greater variability in the financial market
in an earlier period in the middle of the end of 2016 when compared to figure 6
that represents the data of the Ethereum currency.
The
calculated return log for each currency (calculation basis shown in section 3)
was:
Bitcoin: Log = -4416.0380
Ethereum: Log = -2327.7607
6. CONCLUSION
It
is possible to conclude from the historical data that the Bitcoin currency
began to have a significant behavior for the market from August 2017 in
counterpart Etherium began in June 2017. The return series made it possible a
clear visualization that both had a behavior unstable against the market in the
same period between December 2017 and February 2018. The Garch test made it
possible to conclude that the two currencies are not conditional because they
had a persistence result of 1. By the analysis of volatility it can be
concluded that in the period of January 2018 the two currencies had greater
volatility, but when observing more accurately the graph shows that the
currency Bitcoin had greater volatility from the end of the year 2016.
It
is suggested that analyzes with a longer period and a larger number of
currencies be performed for future research.
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