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


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.


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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: <>. Date accessed: 26 july 2024.

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