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

Author

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  • Venelina Nikolova

    (Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

  • Juan E. Trinidad Segovia

    (Department of Accounting and Finance, Faculty of Economics and Business, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

  • Manuel Fernández-Martínez

    (University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT, 30720 Santiago de la Ribera, Región de Murcia, Spain
    These authors contributed equally to this work.)

  • Miguel Angel Sánchez-Granero

    (Department of Mathematics, Faculty of Science, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Venelina Nikolova & Juan E. Trinidad Segovia & Manuel Fernández-Martínez & Miguel Angel Sánchez-Granero, 2020. "A Novel Methodology to Calculate the Probability of Volatility Clusters in Financial Series: An Application to Cryptocurrency Markets," Mathematics, MDPI, vol. 8(8), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1216-:d:389042
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    References listed on IDEAS

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    2. Delia-Elena Diaconaşu & Seyed Mehdian & Ovidiu Stoica, 2022. "An analysis of investors’ behavior in Bitcoin market," PLOS ONE, Public Library of Science, vol. 17(3), pages 1-18, March.
    3. Vadim Azhmyakov & Ilya Shirokov & Luz Adriana Guzman Trujillo, 2024. "Advanced Statistical Analysis of the Predicted Volatility Levels in Crypto Markets," JRFM, MDPI, vol. 17(7), pages 1-15, July.

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