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Journal of Physics: Conference Series
PAPER • OPEN ACCESS
The tail risk measurement of bitcoin price fluctuations under strict
supervision - based on GPD distribution
To cite this article: Juan Wang and Feng Tian 2020 J. Phys.: Conf. Ser. 1437 012069
View the article online for updates and enhancements.
This content was downloaded from IP address 176.9.8.24 on 22/09/2020 at 11:562019 2nd International Symposium on Big Data and Applied Statistics IOP Publishing
Journal of Physics: Conference Series 1437 (2020) 012069 doi:10.1088/1742-6596/1437/1/012069
The tail risk measurement of bitcoin price fluctuations under
strict supervision - based on GPD distribution
Juan Wang1, Feng Tian1*
1
Departments of economics and management, xi 'an university of posts and
telecommunications, China
*
Corresponding author’s e-mail: 2627693252@qq.com
Abstract. The research interval is divided into three intervals according to the date of
occurrence, “China announced to shut down bitcoin exchanges” and “American Securities and
Exchange Commission published the announcement of non-standardization of digital currency
exchanges”. And the Generalized Pareto Distribution is used to measure the tail risk of bitcoin
price fluctuation in the three intervals. It is found that the Generalized Pareto distribution can
better fit the thick tail of the bitcoin yield, and the risk of price fluctuation in the three intervals
presents a change of "low-high-low".
1. Introduction
On September 14, 2017, China announced to shut down bitcoin exchanges. At the same time, bitcoin
prices fell in a short period of time and then rose rapidly. By mid-December 2017, bitcoin price rose to
nearly $20,000. On March 7, 2018, the American Securities and Exchange Commission (SEC) issued
an announcement, which pointed out that there were irregular problems in digital currency trading
platforms. The announcement means that the American regulatory policy on Bitcoin has tightened and
bitcoin price has fallen. HP filtering method is adopted to analyze the overall trend of bitcoin price
changes. As shown in figure 1, the price of bitcoin was on an upward trend in 2017.After March 2018,
the price of bitcoin was on a downward trend.
Hodrick-Prescott Filter (lambda=13322500)
20,000
15,000
12,000
10,000
8,000
5,000
4,000
0
0
-4,000
I II III IV I II III
2017 2018
P Trend Cycle
Figure 1 shows the overall trend of bitcoin price fluctuations
Bitcoin transactions are P2P online transactions, so there is a serious information asymmetry in
bitcoin transactions. This information asymmetry leads to the blind herd mentality of the public,
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd 12019 2nd International Symposium on Big Data and Applied Statistics IOP Publishing
Journal of Physics: Conference Series 1437 (2020) 012069 doi:10.1088/1742-6596/1437/1/012069
resulting in the herding effect in the bitcoin market. The herding effect makes the public make
irrational investment behaviors when they get the market news, which leads to the violent fluctuation
of bitcoin price. The violent fluctuation of bitcoin price makes investors suffer heavy losses and has
serious adverse effects on individuals, society and families. Therefore, it is of great significance to
study the risk of bitcoin price fluctuation.
2. Literature review
Domestic and foreign scholars have conducted a lot of research on bitcoin price and bitcoin market
risk. In terms of the price of bitcoin, the research mainly revolves around the determinants of the price
of bitcoin. In the aspect of bitcoin market risk, a few scholars try to measure the risk of bitcoin market
with financial risk measurement model.
2.1. Research on bitcoin prices
Kristoufek (2014) [1] pointed out that conventional economic factors such as trade demand, supply and
price levels have an important impact on the long-term development of Bitcoin, and the attitude of
governments to Bitcoin plays a decisive role in their fate. Elie Bouri (2018) [3] believes that there is a
right-tail correlation between the global financial stress index and the bitcoin return rate, and Bitcoin
can be used as a safe haven against global financial pressure. Bob Stark (2013) [2] holds the same view
that fiscal policy or monetary policy has limited impact on bitcoin prices, and the most important
determinant is the attitude of governments. Ju Hyun Yu (2019) [4] believes that the growth rate of
Google Trends has a statistically significant effect on the fluctuations in Bitcoin earnings. Donglian
Ma (2019) [5] considered that the daily-week effect in the yield equation varies with the sample period,
while the volatility on Monday and Thursday is significantly higher. Giray Gozgor (2019) [6] argues
that during the period of institutional change, the uncertainty of trade policy has a significant negative
impact on Bitcoin earnings.
2.2. Research on the risk and regulation of the Bitcoin market
Kelly (2018) [22] believes that the “regulatory sandbox” mechanism should be used for reference, and
the “regulatory sandbox” based on observation should be implemented for Bitcoin. Wang Xin (2016)
[23]
believes that virtual currency has four potential risks: money laundering and terrorist financing
risks, consumption risks, financial stability risks and currency stability risks. It should learn from the
supervision experience of foreign virtual currency and implement legislation on Bitcoin. Xu Junjun
(2019) [24] believes that the future of virtual currency has the following regulatory trends.
In general, scholars at home and abroad have done a lot of research on bitcoin. However, the
research on the risk of the bitcoin market is still in its early stage, and there are few studies on the
measurement of the risk of the bitcoin market. This paper analyzes the influence mechanism of strict
regulatory policies on bitcoin price volatility, and measures the extreme risk of bitcoin price volatility
through Generalized Pareto distribution fitting.
3.Empirical analysis
3.1 Selection of variables
According to the purpose of this paper, we need to compare the risk changes of the bitcoin price
fluctuations before and after the event "China closes the Bitcoin exchange" and "American Securities
and Exchange Commission published the announcement of non-standardization of digital currency
exchanges ", so the large interval is selected [2017- 3-14, 2018-9-14], according to the date of
occurrence of the two events, the large interval is divided into three cells, which are the first sub-
interval [2017-3-14, 2017-9-14], and the second Sub-interval [2017-9-14, 2018-3-7], third interval
[2018-3-7, 2018-9-14].
In order to make the variables smoother, logarithmic processing is performed on each subinterval
variable. A first-order difference is made to the bitcoin price of each sub-interval to obtain a sequence
22019 2nd International Symposium on Big Data and Applied Statistics IOP Publishing
Journal of Physics: Conference Series 1437 (2020) 012069 doi:10.1088/1742-6596/1437/1/012069
of yields for each sub-interval. Explore the risk of bitcoin price volatility by analyzing the bitcoin
yield series.
3.2 Normality test
This paper examines the normality of bitcoin yield for each interval by observing the skewness and
kurtosis and the JB statistic.
28 40
Series: DLNP1 Series: DLNP2
24 Sample 3/14/2017 9/14/2017 35 Sample 9/15/2017 3/07/2018
Observations 184 Observations 173
30
20
Mean 0.006228 Mean 0.007094
Median 0.008991 25 Median 0.009451
16 Maximum 0.221475
Maximum 0.223513
20 Minimum -0.190943
Minimum -0.118573
12 Std. Dev. 0.044308 Std. Dev. 0.060990
15
Skewness 0.299945 Skewness 0.011284
8 Kurtosis 6.073057 Kurtosis 4.090068
10
4 Jarque-Bera 75.16056 5 Jarque-Bera 8.568957
Probability 0.000000 Probability 0.013781
0 0
-0.10 -0.05 0.00 0.05 0.10 0.15 0.20 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
FIG. 2 descriptive statistics of bitcoin yield rate in FIG. 3 descriptive statistics of bitcoin yield rate in
the first subinterval the second subinterval
32
Series: DLNP3
28 Sample 3/08/2018 9/14/2018
Observations 190
24
Mean -0.002229
20 Median 0.001648
Maximum 0.127485
16 Minimum -0.106714
Std. Dev. 0.035824
12
Skewness -0.183396
Kurtosis 4.316282
8
4 Jarque-Bera 14.78147
Probability 0.000617
0
-0.10 -0.05 0.00 0.05 0.10
FIG. 4 descriptive statistics of bitcoin yield rate in the third subinterval
3.3 Generalized Pareto distribution fitted bitcoin yield
When fitting Generalized Pareto distribution, the selection of threshold value is very important. In
principle, the selection of threshold should not be too small, the number of overthreshold generally do
not exceed 10% of the sample length. In this paper, the graph of average transcendence function and
the principle of threshold selection are combined to select the threshold.
3.3.1 Generalized Pareto distribution fitting the first interval of bitcoin yield Figure 5 is the average
transcendence function graph of bitcoin yield rate in the first interval. We can see that above the
threshold of 0.0609, the figure shows a straight upward trend, and it can be considered that there is a
fat tail phenomenon. On the basis of the selected threshold value of 0.0609, the GPD distribution
fitting graph of yield rate was made. It can be seen intuitively that the bitcoin yield GPD overthreshold
fitting graph has a good fitting effect, indicating that the use of extreme value theory in the fitting of
GPD distribution in the tail of bitcoin yield has reliability. When the threshold value is 0.0609, there
are 10 sample points beyond the threshold, and at the significance level of 99%, the VAR value is
about -0.0674. Which means the VAR value is -0.0674 under the GPD distribution.
32019 2nd International Symposium on Big Data and Applied Statistics IOP Publishing
Journal of Physics: Conference Series 1437 (2020) 012069 doi:10.1088/1742-6596/1437/1/012069
Fig. 5 average transcendental function graph Fig.6 GPD distribution fit bitcoin yield graph
3.3.2 GPD distribution fitted the second interval bitcoin yield Figure 7 is the average transcendence
function graph of bitcoin yield rate in the second interval. We can see that above the threshold of
0.0998, the figure shows a straight upward trend, and it can be considered that there is a fat tail
phenomenon. On the basis of the selected threshold value of 0.0998, the GPD distribution fitting graph
of yield rate was made. It can be seen intuitively that the bitcoin yield GPD overthreshold fitting graph
has a good fitting effect, indicating that the use of extreme value theory in the fitting of GPD
distribution in the tail of bitcoin yield has reliability. When the threshold value is 0.0998, there are 8
sample points beyond the threshold value. At the significance level of 99%, the VAR value is about -
0.1039. Which means the VAR value is -0.1039 under the GPD distribution.
Fig.7 average transcendental function graph Fig.8 GPD distribution fit bitcoin yield graph
3.3.3 GPD distribution fitting third interval bitcoin yield Figure 10 is the average transcendence
function graph of bitcoin yield rate in the third interval. We can see that above the threshold of 0.0820,
the figure shows a straight upward trend, and it can be considered that there is a fat tail phenomenon.
On the basis of the selected threshold value of 0.0820, the GPD distribution fitting graph of yield rate
was made. It can be seen intuitively that the bitcoin yield GPD overthreshold fitting graph has a good
fitting effect, indicating that the use of extreme value theory in the fitting of GPD distribution in the
tail of bitcoin yield has reliability. When the threshold value is 0.0820, there are 3 sample points
beyond the threshold value. At the significance level of 99%, the VAR value is about -0.0680. Which
means under the VAR value is -0.0680 under the GPD distribution.
42019 2nd International Symposium on Big Data and Applied Statistics IOP Publishing
Journal of Physics: Conference Series 1437 (2020) 012069 doi:10.1088/1742-6596/1437/1/012069
Fig.9 average transcendental function graph Fig.10 GPD distribution fit bitcoin yield graph
4.Conclusion
4.1 GPD distribution can better fit the thick tail of bitcoin yield
The return rate sequence of bitcoin does not obey the normal distribution, and presents the distribution
feature of "thick tail". The GPD distribution in the extreme-value theory is used to fit the thick-tail
feature of bitcoin yield rate, which has reference value to measure the extreme volatility risk of bitcoin
price. It is of reference value for investors and regulators to discuss the risk of bitcoin price fluctuation
from a static perspective, especially for the public who blindly invest in bitcoin.
4.2 Tail risk changes of bitcoin price fluctuations under regulatory policies
The value at risk of the bitcoin yield under the GPD shows “low-high-low” changes in three sub-
intervals. Facts have proved that when the state implements strict regulatory policies, that is, when bad
news strikes, it will have a downward impact on bitcoin prices. Whether it will rebound or not will be
affected by other factors.
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