Value at Risk estimation using GAS models with heavy tailed distributions for cryptocurrencies

Abstract

Risk management and prediction of market losses of cryptocurrencies are of notable value to risk managers, portfolio managers, financial market researchers and academics. One of the most common measures of an asset’s risk is Value-at-Risk (VaR). This paper evaluates and compares the performance of generalized autoregressive score (GAS) combined with heavy-tailed distributions, in estimating the VaR of two well-known cryptocurrencies’ returns, namely Bitcoin returns and Ethereum returns. In this paper, we proposed a VaR model for Bitcoin and Ethereum returns, namely the GAS model combined with the generalized lambda distribution (GLD), referred to as the GAS-GLD model. The relative performance of the GAS-GLD models was compared to the models proposed by Troster et al. (2018), in other words, GAS models combined with asymmetric Laplace distribution (ALD), the asymmetric Student’s t-distribution (AST) and the skew Student’s t-distribution (SSTD). The Kupiec likelihood ratio test was used to assess the adequacy of the proposed models. The principal findings suggest that the GAS models with heavy-tailed innovation distributions are, in fact, appropriate for modelling cryptocurrency returns, with the GAS-GLD being the most adequate for the Bitcoin returns at various VaR levels, and both GAS-SSTD, GAS-ALD and GAS-GLD models being the most appropriate for the Ethereum returns at the VaR levels used in this study.