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Oct 1, 2017
27 cites
The volatility of Bitcoin returns and its correlation to financial markets

Nhi N.Y. Vo, Guandong Xu

The 2008 financial crisis had scattered incredulity around the globe regarding traditional financial systems, which made investors and non-financial customers turn to other alternative such as digital banking systems. The existence and development of blockchain technology make cryptocurrency in recent years believably become a complete alternative to traditional ones. Bitcoin is the world's first peer-to-peer and decentralized digital cash system initiated by Nakamoto [1]. Though being the most prominent cryptocurrency, Bitcoin has not been a legal trading currency in various countries. Its exchange rate has appeared to be an exceptionally high-risk portfolio with extreme volatility, which requires a more detailed evaluation before making any decision. This paper utilizes knowledge of statistics for financial time series and machine learning to (i) fit the parametric distribution and (ii) model and forecast the volatility of Bitcoin returns, and (iii) analyze its correlation to other financial market indicators. The fitted parametric time series model significantly outperforms other standard models in explaining the stylized facts and statistical variances in the behavior of Bitcoin returns. The model forecast also outperforms some machine learning methodologies, which would benefit policy makers, banks and financial investors in trading activities for both long-term and short-term strategies.

Open access
Complex Systems and Time Series Analysis
Financial Risk and Volatility Modeling
Market Dynamics and Volatility
Original source
Oct 1, 2017·Journal of risk and financial management
347 cites
GARCH Modelling of Cryptocurrencies

Jeffrey Chu, Stephen Chan, Saralees Nadarajah, Joerg Osterrieder

With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms of five criteria. Conclusions are drawn on the best fitting models, forecasts and acceptability of value at risk estimates.

Open access
Financial Risk and Volatility Modeling
Market Dynamics and Volatility
Probability and Risk Models
Original source
Aug 15, 2017·Zenodo (CERN European Organization for Nuclear Research)
2 cites
Speculative investment, heavy-tailed distribution and risk management of Bitcoin exchange rate returns

Pedro Bonillo Bueno, Emilio Aragon Fortes, Konstantinos Vlachoski

Since its launch in 2008, Bitcoin becomes one of the most successful and fast-growing alternative currencies. As of 2017, the market capitalization is around $46 billion and arguably expected to continue growing. The Bitcoin to the US dollar exchange rate has been very volatile and fluctuating significantly. Although Bitcoin was designed as a medium of exchange, it is now more as an investment tool and thus the development of effective quantitative risk management tools becomes quite urgent for all the market participants. In this paper, we investigate empirical distribution of the Bitcoin exchange rate returns by using four types of widelyused heavy-tailed distribution and show that the Skewed t distribution has the best empirical performance. We further calculate the VaR based risk measures and found the Skewed t distribution generates the VaR values, which are closest to historical VaR values. Our results could be directly used in the industry’s stress testing practice, and help financial institutions fulfill the regulatory requirements.

Open access
Financial Risk and Volatility Modeling
Market Dynamics and Volatility
Risk and Portfolio Optimization
Original source
Jul 24, 2017·Physica A Statistical Mechanics and its Applications
132 cites
Statistical properties and multifractality of Bitcoin

Tetsuya Takaishi

Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models, and find no evidence of it. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are investigated, confirming that both temporal correlation and the fat-tailed distribution contribute to it. The influence of "Brexit" on June 23, 2016 to GBP--USD exchange rate and Bitcoin is examined in multifractal properties. We find that, while Brexit influenced the GBP--USD exchange rate, Bitcoin was robust to Brexit.

Open access
4 source records
Complex Systems and Time Series Analysis
Financial Risk and Volatility Modeling
Market Dynamics and Volatility
Original source
Jul 12, 2017·arXiv (Cornell University)
6 cites
Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach

Mariusz Tarnopolski

The long-term dependence of Bitcoin (BTC), manifesting itself through a Hurst\nexponent $H>0.5$, is exploited in order to predict future BTC/USD price. A\nMonte Carlo simulation with $10^4$ geometric fractional Brownian motion\nrealisations is performed as extensions of historical data. The accuracy of\nstatistical inferences is 10\\%. The most probable Bitcoin price at the\nbeginning of 2018 is 6358 USD.\n

Open access
3 source records
q-fin.CP
econ.GN
q-fin.ST
Original source
Mar 1, 2017·Annals of Financial Economics
139 cites
A STATISTICAL RISK ASSESSMENT OF BITCOIN AND ITS EXTREME TAIL BEHAVIOR

Joerg Osterrieder, Julian Lorenz

We provide an extreme value analysis of the returns of Bitcoin. A particular focus is on the tail risk characteristics and we will provide an in-depth univariate extreme value analysis. Those properties will be compared to the traditional exchange rates of the G10 currencies versus the US dollar. For investors, especially institutional ones, an understanding of the risk characteristics is of utmost importance. So for Bitcoin to become a mainstream investable asset class, studying these properties is necessary. Our findings show that the bitcoin return distribution not only exhibits higher volatility than traditional G10 currencies, but also stronger non-normal characteristics and heavier tails. This has implications for risk management, financial engineering (such as bitcoin derivatives) — both from an investor's as well as from a regulator's point of view. To our knowledge, this is the first detailed study looking at the extreme value behavior of the cryptocurrency Bitcoin.

Open access
2 source records
Financial Risk and Volatility Modeling
Complex Systems and Time Series Analysis
Market Dynamics and Volatility
Original source
Jan 1, 2017·Journal of Accounting Business and Finance Research
21 cites
GARCH Model With Fat-Tailed Distributions and Bitcoin Exchange Rate Returns

Ruiping Liu, Zhichao Shao, Guodong Wei, Wei Wang

In the era of diminishing power from US dollar and increasing competition among world currencies, Bitcoin, as a completely new concept as a medium of exchange, has received increasing attentions over the world. Nowadays, Bitcoin also becomes an investment vehicle, which carries attractive opportunities but also significant risks for the investment community. In this paper, we have compared the empirical performance of a newly-developed heavy-tailed distribution, the normal reciprocal inverse Gaussian (NRIG), with the most popular heavy-tailed distribution, the Student’s t distribution, under the GARCH framework in fitting the daily Bitcoin exchange rate returns. Our results indicate the heavy-tailed distribution has better performance in capture the daily Bitcoin exchange rate returns dynamics than the standard normal distribution. Our results also show the older fashioned Student’s t distribution still performs better than the new heavy-tailed distribution.

Open access
2 source records
Financial Risk and Volatility Modeling
Market Dynamics and Volatility
Insurance, Mortality, Demography, Risk Management
Original source
Jan 1, 2017·SSRN Electronic Journal
5 cites
Value-at-Risk and Expected Shortfall for the major digital currencies

Stavros Stavroyiannis

Digital currencies and cryptocurrencies have hesitantly started to penetrate the investors, and the next step will be the regulatory risk management framework. We examine the Value-at-Risk and Expected Shortfall properties for the major digital currencies, Bitcoin, Ethereum, Litecoin, and Ripple. The methodology used is GARCH modelling followed by Filtered Historical Simulation. We find that digital currencies are subject to a higher risk, therefore, to higher sufficient buffer and risk capital to cover potential losses.

Open access
2 source records
q-fin.RM
Market Dynamics and Volatility
Financial Risk and Volatility Modeling
Original source
Jan 1, 2017·SSRN Electronic Journal
30 cites
GARCH Modeling of Cryptocurrencies

Jeffrey Chu, Stephen Chan, Saralees Nadarajah, Joerg Osterrieder

No abstract is available for this record.

Open access
Financial Risk and Volatility Modeling
Market Dynamics and Volatility
Complex Systems and Time Series Analysis
Original source
Jan 1, 2017·SSRN Electronic Journal
38 cites
Realized Bitcoin Volatility

Dirk G. Baur, Thomas Dimpfl

No abstract is available for this record.

Open access
Complex Systems and Time Series Analysis
Market Dynamics and Volatility
Financial Risk and Volatility Modeling
Original source
Jan 1, 2017·International Journal of Forecasting
62 cites
Forecasting cryptocurrency volatility

Leopoldo Catania, Stefano Grassi

From the Washington University Senior Honors Thesis Abstracts (WUSHTA), 2017. Published by the Office of Undergraduate Research. Joy Zalis Kiefer, Director of Undergraduate Research and Associate Dean in the College of Arts & Sciences; Lindsey Paunovich, Editor; Helen Human, Programs Manager and Assistant Dean in the College of Arts and Sciences Mentors: Mina Lee and Li Yang

Open access
2 source records
Financial Risk and Volatility Modeling
Complex Systems and Time Series Analysis
Market Dynamics and Volatility
Original source
Jan 1, 2017·Journal of risk and financial management
196 cites
A Statistical Analysis of Cryptocurrencies

Joerg Osterrieder, Stephen Chan, Jeffrey Chu, Saralees Nadarajah

We analyze statistical properties of the largest cryptocurrencies (determined by market capitalization), of which Bitcoin is the most prominent example. We characterize their exchange rates versus the U.S. Dollar by fitting parametric distributions to them. It is shown that returns are clearly non-normal, however, no single distribution fits well jointly to all the cryptocurrencies analysed. We find that for the most popular currencies, such as Bitcoin and Litecoin, the generalized hyperbolic distribution gives the best fit, while for the smaller cryptocurrencies the normal inverse Gaussian distribution, generalized t distribution, and Laplace distribution give good fits. The results are important for investment and risk management purposes.

Open access
2 source records
Complex Systems and Time Series Analysis
Financial Risk and Volatility Modeling
Stochastic processes and financial applications
Original source
Dec 29, 2016·Dynamic Econometric Models
35 cites
Dependency Analysis between Bitcoin and Selected Global Currencies

Beata Szetela, Grzegorz Mentel, Stanisław Gędek

In this research we have tried to identify the relationship between the exchange rate for bitcoin to the leading currencies such as Dollar, Euro, British Pound and Chinese Yuan and Polish zloty as well. We have applied ARMA and GARCH models to model and to analyze the conditional mean and variance. The appliance of GARCH models have identified some dependency in explanation conditional variance between bitcoin and US Dollar, Euro and Yuan, while ARMA analysis have shown no relations between bitcoin and other dependent variables.

Open access
Market Dynamics and Volatility
Complex Systems and Time Series Analysis
Financial Risk and Volatility Modeling
Original source
Nov 4, 2016·Quantitative Finance
71 cites
Model-based pairs trading in the bitcoin markets

P. S. Lintilhac, Agnès Tourin

We propose an optimal dynamic pairs trading strategy model for a portfolio of cointegrated assets. Using stochastic control techniques, we compute analytically the optimal portfolio weights and relate our result to several other strategies commonly used by practitioners, including the static double-threshold strategy. Finally, we apply our model to a bitcoin portfolio and conduct an out-of-sample test with historical data from three exchanges, with two cointegrating relations.

Stochastic processes and financial applications
Financial Markets and Investment Strategies
Financial Risk and Volatility Modeling
Original source