Assessing Financial Risk using Value-At-Risk (VaR) from the perspective of a third world economy, Zimbabwe’s Forex Market
Keywords:
Value at Risk, GARCH Model, Financial Risk, Back testing
Abstract
The Global Financial Depression of 2008 exposed the problems of financial risk estimations in the forex sector and impacted negatively on developing countries. In this paper, the performance of Generalised Autoregressive Conditional Heteroskedasticity (GARCH) family models are used to assess and compared in the estimation of Value at Risk (VaR). The study is based on three major currencies that are used in Zimbabwe’s multiple-currency regime against the USD. The three exchange rates considered are, the ZAR/USD, the EUR/USD, and the GBP/USD. Three univariate types of GARCH models, with the Student’s t and the Normal error distributions, are applied to the three currency indices to ascertain the best VaR estimation formula. Evaluation tests, namely the Violation ratio, Kupiec’s test, and Christoffersen’s test are used to assess the quality of the VaR performance. The GARCH (1, 1) with t-distributed errors produced relatively more accurate computations on the VaR for EUR/USD and GBP/USD at 99% level of significance, while the backtests results were inconclusive for ZAR/USD. The GARCH(1,1) model with t-distributed errors had the lowest Akaike's Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (SBIC) values. The GARCH (1,1) with t-distributed error model is suggested in computing VaR and making other deductions on the capital required. The Global Financial Depression of 2008 exposed the problems of financial risk estimations in the forex sector and impacted negatively on developing countries. In this paper, the performance of Generalised Autoregressive Conditional Heteroskedasticity (GARCH) family models is used to assess and compared in the estimation of Value at Risk (VaR). The study is based on three major currencies that are used in Zimbabwe’s multiple-currency regime against the USD. The three exchange rates considered are, the ZAR/USD, the EUR/USD, and the GBP/USD. Three univariate types of GARCH models, with the Student’s t and the Normal error distributions, are applied to the three currency indices to ascertain the best VaR estimation formula. Evaluation tests, namely the Violation ratio, Kupiec’s test, and Christoffersen’s test are used to assess the quality of the VaR performance. The GARCH (1, 1) with t-distributed errors produced relatively more accurate computations on the VaR for EUR/USD and GBP/USD at 99% level of significance, while the backtests results were inconclusive for ZAR/USD. The GARCH(1,1) model with t-distributed errors had the lowest Akaike's Information Criterion (AIC) and Schwarz’s Bayesian Information Criterion (SBIC) values. The GARCH (1,1) with t-distributed error model is suggested in computing VaR and making other deductions on the capital required.References
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6. Christoffersen, P. (1998). Evaluating Interval Forecasts, International Economic Review, 39(4):841-862
7. Engle, R. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4): 987-1007
8. Franco, C. and Zakoian, J. (2010). GARCH Models. Structure, Statistical Inference and Financial Applications. WILEY, London.
9. Glosten, L., Jagannathan, R. and Runkle, D. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance, XLVIII:1779-1801
10. Nelson, D. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59(2):347-370
11. Terasvirta, T. (2006). An Introduction to Univariate GARCH Models, SSE/EFI Working papers in Economics and Finance, 646Kupiec, P.H. (1995). Techniques for verifying the accuracy of risk measurement models. The Journal of Derivatives, 3, 73-84.
12. Nikolic-Djoric, E., & Djoric, D. (2011). Dynamic value at risk estimation for BELEX15. Metodološki zvezki, 8, 79–98. Retrieved from http://www.stat-d.si/mz/
13. Bucevska, V. (2012). An Empirical evaluation of GARCH models in value-at-risk estimation: Evidence from the Macedonian stock exchange. Business Systems Research, 4, 49–64.
14. .Miletic, M. & Miletic, S. (2015). Performance of value at risk models in the midst of the global financial crisis in selected CEE emerging capital markets. Economic Research-Ekonomska Istraživanja, 28, 132–166.
15. Bollerslev, T. (1987). A Conditional Heteroscedasticity Time Series Model for Speculative Prices and Rates of Return, The Review of Economics and Statistics, 69 (3): 542–547
16. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31:307-327.
2. Danielsson, J. (2011). Financial Risk Forecasting. WILEY, London.
3. https://www.investing.com/currencies/
4. Dowd, K. (2002). Measuring market risk. WILEY, London.
5. Mladenovic Z., Miletic M., & Miletic S. (September 2012). Value at risk in European emerging economies: An empirical assessment of financial crisis period. University of Belgrade, Faculty of Economics.
6. Christoffersen, P. (1998). Evaluating Interval Forecasts, International Economic Review, 39(4):841-862
7. Engle, R. (1982). Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50(4): 987-1007
8. Franco, C. and Zakoian, J. (2010). GARCH Models. Structure, Statistical Inference and Financial Applications. WILEY, London.
9. Glosten, L., Jagannathan, R. and Runkle, D. (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks, Journal of Finance, XLVIII:1779-1801
10. Nelson, D. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach, Econometrica, 59(2):347-370
11. Terasvirta, T. (2006). An Introduction to Univariate GARCH Models, SSE/EFI Working papers in Economics and Finance, 646Kupiec, P.H. (1995). Techniques for verifying the accuracy of risk measurement models. The Journal of Derivatives, 3, 73-84.
12. Nikolic-Djoric, E., & Djoric, D. (2011). Dynamic value at risk estimation for BELEX15. Metodološki zvezki, 8, 79–98. Retrieved from http://www.stat-d.si/mz/
13. Bucevska, V. (2012). An Empirical evaluation of GARCH models in value-at-risk estimation: Evidence from the Macedonian stock exchange. Business Systems Research, 4, 49–64.
14. .Miletic, M. & Miletic, S. (2015). Performance of value at risk models in the midst of the global financial crisis in selected CEE emerging capital markets. Economic Research-Ekonomska Istraživanja, 28, 132–166.
15. Bollerslev, T. (1987). A Conditional Heteroscedasticity Time Series Model for Speculative Prices and Rates of Return, The Review of Economics and Statistics, 69 (3): 542–547
16. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31:307-327.
Published
2025-06-23
How to Cite
Chikobvu , Delson, & Ndlovu, T. (2025). Assessing Financial Risk using Value-At-Risk (VaR) from the perspective of a third world economy, Zimbabwe’s Forex Market. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-1307
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Section
Research Articles
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