Predicting Value-at-Risk of Bitcoin and Ethereum Using Extreme Value Theory

  • Wendy Shinyie Ling Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia
  • Si Yin Tan Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia
  • Fong Peng Lim Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Malaysia

Abstract

Extreme value theory (EVT) has been widely used in finance especially when extreme events such as crashes, brakes and peaks occur. EVT focuses on extreme events or situations, which are typically referred to as outliers, and is able to provide better estimation for risk models. Cryptocurrency is a popular but high-risk investment due to its high volatility and occurrence of extreme events. It is difficult and critical to predict the return of cryptocurrency, mainly because of its extreme nature. This research employs two different EVT approaches, namely, block maxima approach and peaks over threshold approach, are used to model the daily extreme returns of Bitcoin and Ethereum by encrypting the left tail of cryptocurrency return distributions. Apart from that, Value-at- Risk (VaR) plays an important role in estimating the investment risk in the financial sector. Therefore, before investing, it is very important to assess the risk of cryptocurrency. In this study, VaR is evaluated by using the age-weighted historical simulation method and normal distribution. This study finds that generalized extreme value distribution using the block maxima approach fits the cryptocurrencies returns data better and normal distribution outperformed other distributions in estimating VaR. In addition, the return levels of Bitcoin and Ethereum indicates that the biggest potential losses that Ethereum will face in the next 100 years is 105.02% higher than that of Bitcoin. The result of VaR estimation also shows that the risk of Ethereum is higher than that of Bitcoin, because its high risk values are 7.03% and 8.46% respectively. The findings in this study can assist investors in understanding the behaviour of the tails in the cryptocurrency market and in making financial decisions.

References

Ali, N., Zaimi, N. N., & Ali, N. M. (2020). Statistical modelling of Malaysia trading gold price using extreme value theory approach. Advances in Mathematics: Scientific Journal, 10(1), 9–18.
Ashford, K., & Schmidt, J. (2022). What is cryptocurrency. Forbes Advisor, 23.
Balkema, A. A. & de Haan, L. (1974). Residual life time at great age. Ann Probab, 2:792–804.
Cao, V. T. H. & Johansson, A. (2022). Risk measurement of cryptocurrencies using value at risk and expected shortfall [Unpublished master’s thesis]. Lund University.
Dowd, K. (2005). Measuring market risk. John Wiley & sons, Ltd.
Farell, P. J., & Stewart, K. R. (2006). Comprehensive study of test for normality and symmetry:Extending the Spiegelhalter test. Journal of Statistical Computation and Simulation, 76(9), 803–816.
Gkillas, K., & Katsiampa, P. (2018). An application of extreme value theory to cryptocurrencies. Economics Letters, 164, 109–111.
Glaser, F., Zimmermann, K., Haferkorn, M., Weber, M. C., & Siering, M. (2014). Bitcoin-asset or currency? Revealing users' hidden intentions. Revealing Users' Hidden Intentions.
Gnedenko, B. (1943). Sur la distribution limite du terme maximum d’une serie aleatoire. Ann Math,44(3), 423–453.
Gupta, M. (2017). Blockchain for dummies. IBM Limited Edition. John Wiley & Sons, Inc.
Hoboken, NJ.Hosking, J. R. (1990). L‐moments: Analysis and estimation of distributions using linear
combinations of order statistics. Journal of the royal statistical society: Series B (methodological), 52(1), 105–124.
Hussain, S. I., Masseran, N., Ruza, N., & Safari, M. A. M. (2021). Predicting extreme returns ofbitcoin: Extreme value theory approach. In Journal of Physics: Conference Series, 1988(1), IOP Publishing.
Islam, M. T., & Das, K. P. (2021). Predicting Bitcoin return using extreme value theory. American Journal of Mathematical and Management Sciences, 40(2), 177–187.
Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of meteorological elements. Quarterly Journal of the Royal Meteorological Society, 81(348), 158–171
Published
2023-11-19
How to Cite
LING, Wendy Shinyie; TAN, Si Yin; LIM, Fong Peng. Predicting Value-at-Risk of Bitcoin and Ethereum Using Extreme Value Theory. Menemui Matematik (Discovering Mathematics), [S.l.], v. 45, n. 2, p. 152-176, nov. 2023. ISSN 0126-9003. Available at: <https://myjms.mohe.gov.my/index.php/dismath/article/view/24491>. Date accessed: 26 july 2024.

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.