Cryptos have rough volatility and correlated jumps

Lukas Krain (), Xiaorui Zuo () and Wolfgang Karl Härdle ()
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Lukas Krain: Humboldt-Universität zu Berlin
Xiaorui Zuo: National University of Singapore
Wolfgang Karl Härdle: Humboldt-Universität zu Berlin

Digital Finance, 2025, vol. 7, issue 2, No 5, 275-294

Abstract: Abstract Contrary to expectations some years ago, the crypto market has matured and gives the impression of an established financial eco-system. Certainly, some deviations from robustness, typically reflected in event related volatility bursts and spikes, are observed, but a liquid derivatives market has been established, at least for the dominant digital assets. It is, therefore, not only necessary for pricing contingent claims to understand the stochastic dynamics via a solid data analysis but also to provide instruments identifying volatility patterns and their dynamic evolvement. Using the Bitcoin as a representative instrument, we ventured to model this particular crypto coin dynamics via a combination of roughness in volatility and jumps in the underlying crypto currency. Findings on the roughness, e.g. the size of the Hurst exponent for the volatility dynamics, revealed remarkable differences when compared to corresponding estimates for equities and fixed income funds. Through a parametric bootstrap, we give evidence that both roughness and jumps are crucial for predicting the range of next-day returns in terms of a simulated confidence interval. By scaling up the jump sizes, we obtained a nicely working combination of volatility roughness and jumps (of the underlying) resulting in precise coverage levels. All calculations may be redone on quantlet.com and courselets are in .

Keywords: Cryptos; Rough volatility; Jumps; Hurst exponent; Hawkes process (search for similar items in EconPapers)
JEL-codes: C02 C53 C58 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42521-025-00125-8

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