Estimating Extreme Value at Risk Using Bayesian Markov Regime Switching GARCH-EVT Family Models

Abstract

In this study, the performance of the Bayesian Markov regime-switching GARCH-EVT in the estimation of extreme value at risk in the BitCoin/dollar (BTC/USD) and the South African Rand/dollar (ZAR/USD) exchange rates is investigated. The goal is to capture regime switches and extreme returns to exchange rates, all to explain and compare the riskiness of BitCoin and the Rand. The Markov chain Monte Carlo method is used to estimate parameters for the GARCH family models. Using the deviance information criterion, the two regime-switching GARCH models perform better than the single-regime GARCH model when modelling volatility of the two currencies’ returns. Based on the estimated value at risk figures, BitCoin is riskier than the Rand. At both 95% and 99% levels of significance, the results suggest that the MS(2)-gjrGARCH(1,1)-GEVD7 and MS(2)-sGARCH(1,1)-GPD7 are the best fitting models for both BTC/USD and ZAR/USD respectively, at both significance levels. The backtest confirms model adequacy. This information is useful to local and foreign currency traders and investors who need to fully appreciate the risk exposure when they convert their savings or investments to BitCoin instead of the South African currency, the Rand.