Statistical Analysis of the Exchange Rate of Bitcoin

Chu, Jeffrey; Nadarajah, Saraless; Chan, Stephen

doi:10.1371/journal.pone.0133678

Cited by 152 publications

(99 citation statements)

References 59 publications

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“…The question arises which parametric distribution can characterize the Bitcoin exchange rate. In Chu et al (2015), it is shown that the generalized hyperbolic distribution gives the best maximum-likelihood fit among a large set of parametric distributions. In Osterrieder (2017), the author shows that the asymmetric Student's t-distribution is the best descriptor for the returns of the most important cryptocurrencies, choosing from a reasonably large set of heavytailed distributions.…”

Section: Motivation and Normal Distributionmentioning

confidence: 99%

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A Statistical Risk Assessment of Bitcoin and Its Extreme Tail Behavior

Osterrieder

Lorenz²

2017

Ann. Finan. Econ.

119

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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.

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Section: Motivation and Normal Distributionmentioning

confidence: 99%

“…For a discussion of the normal distribution of exchange rates, see Coppes (1995). Corlu and Corlu (2015) and Chu et al (2015) discuss parametric approaches to modeling exchange rate returns. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

A Statistical Risk Assessment of Bitcoin and Its Extreme Tail Behavior

Osterrieder

Lorenz²

2017

Ann. Finan. Econ.

119

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“…Short and long term links are found, and Bitcoin is shown to exhibit the properties of both standard financial assets but also speculative assets, which fuel further discussion on whether Bitcoin should be classed as a currency, asset or an investment vehicle. Chu et al (2015) give the first statistical analysis of the exchange rate of Bitcoin. They fit fifteen of the most common distributions used in finance to the log returns of the exchange rate of Bitcoin versus the U.S. Dollar.…”

Section: Introductionmentioning

confidence: 99%

A Statistical Analysis of Cryptocurrencies

Chan¹,

Chu²,

Nadarajah³

et al. 2017

JRFM

Self Cite

139

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Abstract: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.

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“…[4] fitted the Student's t, asymmetric Student's t, hyperbolic, generalized hyperbolic, generalized Lambda, skew t, normal inverse Gaussian and normal distributions to the data. [2] has fitted both heavy tailed and light-tailed distributions to the Bitcoin exchange rate: The normal, logistic, Laplace, exponential power, skew normal, skewed exponential power and asymmetric exponential power distributions have light tails. The Student's t, skew t, generalized t, skewed Student's t, asymmetric Student's t, normal inverse gamma, hyperbolic and generalized hyperbolic distributions have heavy tails.…”

Section: Heavy-tailed Distributionsmentioning

confidence: 99%

“…Some of the papers are: [3,4,5,6,7,8,9,10,11,12,13]. Probably the most comprehensive collection of distributions used to analyze any exchange rate data set is given by [2]. Each distribution was fitted by the method of maximum likelihood.…”

Section: Heavy-tailed Distributionsmentioning

confidence: 99%

The Statistics of Bitcoin and Cryptocurrencies

Osterrieder¹

2017

Proceedings of the 2017 International Conference on Economics, Finance and Statistics (ICEFS 2017)

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Abstract. Cryptocurrencies became popular with the emergence of Bitcoin and have shown an unprecedented growth over the last few years. As of November 2016, more than 720 cryptocurrencies exist, with Bitcoin still being the most popular one. We show the statistical properties of the most important cryptocurrencies. We characterize their exchange rates versus the US Dollar by fitting parametric distributions to them, including the Student t distribution, the generalized hyperbolic distribution as well as the asymmetric normal inverse Gaussian and the asymmetric variance gamma distribution. Our findings show that cryptocurrencies exhibit strong non-normal characteristics, with standard heavy-tailed distributions such as the Student t distribution giving good descriptions of the data. This is the first study that looks at the parametric distribution of cryptocurreny returns. The results are important for investment and risk management purposes.

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Statistical Analysis of the Exchange Rate of Bitcoin

Cited by 152 publications

References 59 publications

A Statistical Risk Assessment of Bitcoin and Its Extreme Tail Behavior

A Statistical Risk Assessment of Bitcoin and Its Extreme Tail Behavior

A Statistical Analysis of Cryptocurrencies

The Statistics of Bitcoin and Cryptocurrencies

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