Abstract
This paper develops the ability of the normal inverse Gaussian distribution (NIG) to fit the returns of bitcoin (BTC). As the first cryptocurrency created, the behavior of this new asset is characterized by great volatility. The lack of a proper definition or classification under existing theory exacerbates this property in such a way that explosive periods followed by a rapid decline have been observed along the series, meaning bubble episodes. By detecting the periods in which a bubble rises and collapses, it is possible to study the statistical properties of such segments. In particular, adjusting a theoretical distribution may help to determine better strategies to hedge against these episodes. The NIG is an appropriate candidate not only because of its heavy-tailed property but also because it has been proven to be closed under convolution, a characteristic that can be implemented to measure multivariate value at risk. Using data on the price of BTC with respect to seven of the main global currencies, the NIG was able to fit every time segment despite the bubble behavior. In the out-of-sample tests, the NIG was proven to have an adjustment similar to that of a generalized hyperbolic (GH) distribution. This result could serve as a starting point for future studies regarding the statistical properties of cryptocurrencies as well as their multivariate distributions.
Highlights
The dawn of the XXI century has been characterized by high technological development by technology permeating through different areas of human interaction
Using the Broyden–Fletcher–Goldfarb– Shanno (BFGS) algorithm under maximum likelihood estimation (MLE) criteria, the four parameters left are obtained by this quasi-Newton method
Perhaps the most notable innovation as well as the riskiest is the development of new currencies backed only by mathematical cryptography and operated through computational devices
Summary
The dawn of the XXI century has been characterized by high technological development by technology permeating through different areas of human interaction. One of these implementations is known as cryptocurrencies, which is term under which different financial assets are categorized. Even when there is no government or financial institution that recognizes cryptocurrencies as a means of payment for goods or services, many of them have seen an increase in demand in recent years [2]. Bitcoin (BTC) is considered the most important cryptocurrency, being the first to be created and having nearly 40% of the total cryptocurrency market cap on May 15th, 2018. BTCs creation dates back to the 2008 financial crisis. Public sentiment tended toward discontent about how the economy was being directed and the impact that political
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