A Wavelet-Decomposed WD-ARMA-GARCH-EVT Model Approach to Comparing the Riskiness of the BitCoin and South African Rand Exchange Rates

Abstract

In this paper, a hybrid of a Wavelet Decomposition–Generalised Auto-Regressive Conditional Heteroscedasticity–Extreme Value Theory (WD-ARMA-GARCH-EVT) model is applied to estimate the Value at Risk (VaR) of BitCoin (BTC/USD) and the South African Rand (ZAR/USD). The aim is to measure and compare the riskiness of the two currencies. New and improved estimation techniques for VaR have been suggested in the last decade in the aftermath of the global financial crisis of 2008. This paper aims to provide an improved alternative to the already existing statistical tools in estimating a currency VaR empirically. Maximal Overlap Discrete Wavelet Transform (MODWT) and two mother wavelet filters on the returns series are considered in this paper, viz., the Haar and Daubechies (d4). The findings show that BitCoin/USD is riskier than ZAR/USD since it has a higher VaR per unit invested in each currency. At the 99% significance level, BitCoin/USD has average values of VaR of 2.71% and 4.98% for the WD-ARMA-GARCH-GPD and WD-ARMA-GARCH-GEVD models, respectively; and this is slightly higher than the respective 2.69% and 3.59% for the ZAR/USD. The average BitCoin/USD returns of 0.001990 are higher than ZAR/USD returns of −0.000125. These findings are consistent with the mean-variance portfolio theory, which suggests a higher yield for riskier assets. Based on the p-values of the Kupiec likelihood ratio test, the hybrid model adequacy is largely accepted, as p-values are greater than 0.05, except for the WD-ARMA-GARCH-GEVD models at a 99% significance level for both currencies. The findings are helpful to financial risk practitioners and forex traders in formulating their diversification and hedging strategies and ascertaining the risk-adjusted capital requirement to be set aside as a cushion in the event of the occurrence of an actual loss.