Cryptos Have Rough Volatility and Correlated Jumps
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 quantinar.com
Wolfgang Karl HÄRDLE attained his Dr. rer. nat. in Mathematics at Universität Heidelberg in 1982 and in 1988 his habilitation at Universität Bonn. He is Ladislaus von Bortkiewicz Professor of Statistics at Humboldt-Universität zu Berlin and the director of the Sino German Graduate School (洪堡大学 + 厦门大学) IRTG1792 on “High dimensional non stationary time series analysis”. He directs IDA Institute for Digital Assets,
University of Economic Studies, Bucharest, RO. His research focuses on data analytics, dimension reduction and quantitative finance. He has published over 30 books and more than 300 papers in top statistical, econometrics and finance journals. He is highly ranked and cited on Google Scholar, REPEC and SSRN. He has professional experience in financial engineering, S.M.A.R.T. (Specific, Measurable, Achievable, Relevant, Timely) data analytics, machine learning and cryptocurrency markets. He has created the www.quantlet.com platform, a cryptocurrency index, CRIX www.royalton-crix.com He is 玉山学者 (Yushan Scholar), web page hu.berlin/wkh