The global foreign exchange market is undoubtedly the world's biggest market with huge
trading volume, surpassing other markets including equities and commodities. This study focuses on
exchange rate modelling where we perform an empirical study to evaluate models which can be used
to identify a common Value at Risk (VaR) model for fourteen African currencies. The descriptive
statistics of our data reveal the salient features common to financial time series which are nonnormality,
high kurtosis, skewness and presence of heteroscedasticity except for one currency, the
central African CFA Franc. The latter is excluded from the modelling exercise. We make use of
GARCH, GJR-GARCH and FIGARCH to model volatility using four distributions: normal, student-t,
GED and skew-t. Unconditional EVT and dynamic GARCH-EVT methodologies are also used for
volatility modelling; both with static (S) and rolling windows (R). Results show that static window
shows a better performance than rolling window. Unconditional EVT is seen to overpredict VaR and
dynamic EVT is not among the best models. The GARCH (33.3%) and GJR-GARCH (38.5%) models
produce better forecasts with a dominance for GJR-GARCH models. Despite the data being skewed,
the normal distribution gives better forecast. We also observe that GARCH-S-Normal is suitable for
Southern African Development Community (SADC) and FIGARCH for East African Community
(EAC) countries. A geographical combination reveals the use of GJR-GARCH for Northern and
Western African regions and GARCH-S-Normal for South African region. Despite not finding a unique
model for all countries, it is interesting to note that different regions/communities can adopt a common
Value at Risk model for forecasting purposes. Our results provide a full validation of the models under
the different backtesting methods and thus could be implemented at the practitioner’s level.
Review of Economic Studies, 58, pp. 565-585.
Balkema, A.A. & De Haan, L. (1974). Residual life time at great age. The Annals of Probability, 2(5),
Bedowska-Sojka, B. (2015). Daily VaR Forecasts with Realized Volatility and GARCH Models.
Argumenta Oeconomica, 34, 1, pp. 157-173.
Bollerslev, T. (1986). Generalised Autoregressive Conditional Heteroscedasticity. Journal of
Econometrics, 31, pp. 307-327.
Bollerslev, T.; Engle, R.F. & Woolridge, J.M. (1988). A capital asset pricing model with time varying
covariances. Journal of Political Economy, 96, pp. 116–131.
Brooks, C. & Burke, S.P. (1998). Forecasting exchange rate volatility using conditional variance
models selected by information criteria. Economics Letters, 61, pp. 273-278.
Carvalhal, A. & Mendes, B.V.M. (2003). Value-at-Risk and Extreme Returns in Asian Stock Markets.
International Journal of Business, 8, 1, Available at SSRN: https://ssrn.com/abstract=420266 or
Chong, C.W.; Chun, L.S. & Ahmad, M.I. (2002). Modelling the Volatility of Currency Exchange Rate
Using GARCH Model. Pertanika Journal of Social Science & Humanities, 10 (2), pp. 85-95.
Christoffersen, P. (1998). Evaluating Interval Forecasts. International Economic Review, 39, pp. 841-
Jesus, R.; Ortiz, E. & Cabello, A. (2013). Long run peso/dollar exchange rates and extreme value
behavior: Value at Risk modeling. The North American Journal of Economics and Finance, 24, pp.
Degiannakis, S.; Floros, C. & Dent, P. (2013). Forecasting value at risk and expected shortfall using
fractionally integrated models of conditional volatility: International evidence. International Review of
Financial Analysis, 27, pp. 21-23.
Emenike, K.O. (2010). Modelling Stock Returns Volatility In Nigeria Using GARCH Models. MPRA
Paper 22723, University Library of Munich, Germany. Retrieved from https://mpra.ub.unimuenchen.
Farhat I. (2016). Risk Forecasting of Karachi Stock Exchange: A Comparison of Classical and Bayesian
GARCH models. Pakistan Journal of Statistics and Operation Research, 12, 3, pp. 453-465.
Fernandez, V. (2003). Extreme Value Theory and Value at Risk. Revista de Análisis Económico, 18
(1), pp. 57-85.
Gencay, R. & Selcuk, F. (2004). Extreme value theory and value-at-risk: relative performance in
emerging markets. International Journal of Forecasting, 20 (2), pp. 287-303.
Gilli, M. & Kellezi, E. (2006). An Application of Extreme Value Theory for Measuring Financial Risk.
Computational Economics, 27 (2-3), pp. 207-228.
Glosten, L.R.; Jagannathan, R. & Runkle, D.E. (1993). On the Relation between the Expected Value
and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance, 48 (5), pp. 1779-1801.
Gonpot, P.N. & Chung, J.P. (2016). Risk model validation for BRICS countries: a value-at-risk,
expected shortfall and extreme value theory approach. Journal of Risk Model Validation, 9(3), pp. 1-
Hill, B. (1975). A simple general approach to inference about the tail of a distribution. The Annals of
Statistics, 3, pp. 1163–1174.
Huang, H.C.; Su, Y.C. & TSUI, J.T. (2015). Asymmetric GARCH Value-at-Risk over MSCI in
Financial Crisis. International Journal of Economics and Financial Issues, 5(2), pp. 390-398.
Johanssen, A. & Sowa, V. (2013). A comparison of GARCH models for VaR estimation in three
different markets. Thesis. Uppsala University .Retrieved from http://www.divaportal.
org/smash/record.jsf?pid=diva2%3A630568&dswid=-4971, date: 04.09.2018.
Jorion, P. (2002). Value at Risk: The New Benchmark for managing Financial Risk. 2nd Ed. Singapore:
Mc Graw Hill.
Kutu, A.A & Ngalawa, H. (2017). Modelling Exchange Rate Volatility and Global Shocks in South
Africa. Acta Universitatis Danibius, 13, 3, pp. 178-193.
Lopez, J.A. (1999). Methods for Evaluating Value-at-Risk Estimates. Federal Reserve Bank of New
York, Economic Policy Review, 2, 3-39. Retrieved from
Mabrouk, S. (2016). Forecasting Financial Assets Volatility Using Integrated GARCH-Type Models:
International Evidence. Journal of Finance and Economics, 4 (2), pp. 54 - 62.
Mc Neil, A.J. & Frey, R. (2000). Estimation of tail-related risk measures for heteroscedastic financial
time series: an extreme value approach. Journal of Empirical Finance, 7(3–4), pp. 271-300.
Neftci, S.N. (2000). Value at risk calculations, extreme events, and tail estimation. Journal of
Derivatives, 7, pp. 23–38.
Nieppola, O. (2009). Backtesting Value-at-Risk Models. Thesis (PhD). Helsinki School of Economics.
wed=y, date: on 03.09.2018.
Petrica, A.C. & Stancu, S. (2017). Empirical Results of Modeling EUR/RON Exchange Rate using
ARCH, GARCH, EGARCH, TARCH and PARCH models. Romanian Statistical Review nr. 1.
Pickands, J. (1975). Statistical inference using extreme order statistics. Annals of Statistics, 3, pp. 119–
So, M.K.P. & Yu, P.L.H. (2005). Empirical Analysis of GARCH models in value at risk estimation.
Journal of International Financial Markets, Institutions and Money, 16(2), pp. 180-197. Abstract only.
Tsay, R.S. (2002). Analysis of Financial Time Series, 2nd ed. New Jersey: John Wiley & Sons INC.,
Vilasuso, J. (2002). Forecasting exchange rate volatility, Economics Letters, 76, pp. 59-64.
Wang, Z.R.; Wu, W.T.; Chen, C. & Zhou, Y.J. (2010). The exchange rate risk of Chinese yuan: Using
VaR and ES based on extreme value theory. .Journal of Applied Statistics, 37, pp. 265-282.
The author fully assumes the content originality and the holograph signature makes him responsible in case of trial.