A Novel Methodology to Calculate the Probability of Volatility Clusters in Financial Series: An Application to Cryptocurrency Markets

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2020
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Abstract
One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a novel methodology to calculate the probability of volatility clusters with a special emphasis on cryptocurrencies. With this aim, we calculate the Hurst exponent of a volatility series by means of the FD4 approach. An explicit criterion to computationally determine whether there exist volatility clusters of a fixed size is described. We found that the probabilities of volatility clusters of an index (S&P500) and a stock (Apple) showed a similar profile, whereas the probability of volatility clusters of a forex pair (Euro/USD) became quite lower. On the other hand, a similar profile appeared for Bitcoin/USD, Ethereum/USD, and Ripple/USD cryptocurrencies, with the probabilities of volatility clusters of all such cryptocurrencies being much greater than the ones of the three traditional assets. Our results suggest that the volatility in cryptocurrencies changes faster than in traditional assets, and much faster than in forex pairs.
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nikolova2020mathematicsa Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Venelina Nikolova;Juan E. Trinidad Segovia;Manuel Fernández-Martínez;Miguel Angel Sánchez-Granero;Nikolova, Venelina;Trinidad Segovia, Juan E.;Fernández-Martínez, Manuel;Sánchez-Granero, Miguel Angel;
Journal Mathematics
Year 2020
DOI
10.3390/math8081216
URL
https://www.mdpi.com/2227-7390/8/8/1216/htm
Keywords
bitcoin ethereum volatility cluster hurst exponent fd4 approach volatility series probability of volatility cluster s&amp p500 ripple

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