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.
Highlights
It is easy to observe that large fluctuations in stock market prices are followed by large ones, whereas small fluctuations in prices are more likely to be followed by small ones
One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates, and the high risk associated with their use
The authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent [2]
Summary
It is easy to observe that large fluctuations in stock market prices are followed by large ones, whereas small fluctuations in prices are more likely to be followed by small ones. Agent-based models allow reproducing and explaining some stylized facts of financial markets [12]. Raberto et al [17] introduced an agent-based artificial market whose heterogeneous agents exchange only one asset, which exhibits some key stylized facts of financial markets They found that the volatility clustering effect is sensitive to the model size, i.e., when the number of operators increases, the volatility clustering effect tends to disappear. Shi et al [26] explained volatility clustering through a model of security price dynamics with two kind of participants, namely speculators and fundamental investors They considered that information arrives randomly to the market, which leads to changes in the viewpoint of the market participants according to a certain ratio.
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