Abstract
A country’s level of exchange risk is closely linked to its financial stability, on a macro-economic scale. South African exchange rates, in particular, have a significant impact on imports, inflation, consumer prices and monetary policies. Consequently, it is imperative for economists and investors to assess accurately the associated exchange risks. Exchange rates, like most financial time series, are leptokurtic and contradict the classical Gaussian assumption. We therefore introduce subclasses of the generalised hyperbolic distribution as alternative models and contrast these with the normal distribution. We conclude that the variance-gamma model is the most robust for describing the log-returns of daily USD/ZAR exchange rates and their related Value-at-Risk (VaR) estimates. The model selection methodologies utilised in our analyses include the robust Kolmogorov-Smirnov test and the Akaike information criterion. Backtesting on the adequacy of VaR estimates is also performed using the Kupiec likelihood ratio test.
Highlights
A country’s level of exchange risk is closely linked to its financial stability, on a macro-economic scale
The main contributions made by this article are as follows: firstly, we identify the variancegamma (VG) distribution as the most suitable subclass of generalised hyperbolic distributions (GHDs) for describing daily US dollar (USD)/ZAR (ZAR is the South African rand) exchange rate log-returns, using statistical methods such as the robust Kolmogorov-Smirnov goodness-of-fit test and the Akaike information criterion
In this research we have provided assessments of the adequacy of generalised hyperbolic distributions (GHDs) for modelling the USD/ZAR exchange rate
Summary
“Exchange rate” can be defined as the value of a country’s currency expressed in terms of another country’s currency. Aas and Haff (2006) showed that the logarithmic returns of the /EUR (NOW is the Norwegian Krone) exchange rate has a heavier right tail than a left one, with the latter behaving more like the Gaussian distribution They proposed the use of generalised hyperbolic (GH) skew Student’s t distribution and observed that it provides a better fit than the normal-inverse Gaussian distribution and the skew t distribution proposed by Azzalini and Capitanio (2003). The main contributions made by this article are as follows: firstly, we identify the variancegamma (VG) distribution as the most suitable subclass of GHDs for describing daily USD/ZAR (ZAR is the South African rand) exchange rate log-returns, using statistical methods such as the robust Kolmogorov-Smirnov goodness-of-fit test and the Akaike information criterion.
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