Back
 JFRM  Vol.10 No.3 , September 2021
Modeling Bank of Kigali Stock Risks in Rwanda Stock Exchange Using Extreme Value Distribution
Abstract: Extreme Value Theory has come forth as one of the most significant probability theories in applied sciences. Modeling extreme events has always been of interest in many disciplines such as hydrology, insurance, and finance. This study seeks to model the Bank of Kigali’s (BK) stock risks in Rwanda stock exchange using Extreme Value Distribution. Two major approaches are used. To model Bank of Kigali stock risks, the Generalised Extreme Value Distribution (GEVD), precisely the Block Maxima is implemented. To examine its associated exceedances, the Generalised Pareto Distribution (GPD) is also implemented. Risk measures considered are the Value at Risk (VaR) and the Expected Shortfalls (ES). Findings reveal that the Frechet distribution fits reasonably well the distribution of the BK stock returns and GPD the exceedances. Also, the risk measures such as Value at Risk and Expected shortfall were computed with high level (99.5%) quantiles to serve as a guide to investors to make a decision as to whether to invest in Bank of Kigali’s stock or not. The findings show that GPD fits the tail of the data well.
Cite this paper: Edem, K. and Ndengo, M. (2021) Modeling Bank of Kigali Stock Risks in Rwanda Stock Exchange Using Extreme Value Distribution. Journal of Financial Risk Management, 10, 225-240. doi: 10.4236/jfrm.2021.103013.
References

[1]   Altar, M., Ifrim, A., Altar-Samuel, A. N., Chang, T. Y., Hao, F. A. N. G., Yen-Hsien, L. E. E., Yuchen, W., Dumitrescu, B. A. et al. (2015). Analysis and Surveys. Romanian Journal of Economic Forecasting, 18.

[2]   Bi, G., & Giles, D. E. (2007). An Application of Extreme Value Analysis to Us Movie Box Office Returns. In Proceedings of the 2007: International Congress on Modelling and Simulation: Land, Water and Environmental Management: Integrated Systems for Sustainability (pp. 2652-2658). Citeseer.

[3]   Bommier, E. (2014). Peaks-over-Threshold Modelling of Environmental Data.

[4]   Castillo, E., Hadi, A. S., Balakrishnan, N., & Sarabia, J.-M. (2005). Extreme Value and Related Models with Applications in Engineering and Science (Vol. 25, 362 p). Wiley.

[5]   Chou, H.-C., & Wang, D. K. (2014). Estimation of Tail-Related Value-at-Risk Measures: Range Based Extreme Value Approach. Quantitative Finance, 14, 293-304.
https://doi.org/10.1080/14697688.2013.819113

[6]   Daníelsson, J., Morimoto, Y. et al. (2000). Forecasting Extreme Financial Risk: A Critical Analysis of Practical Methods for the Japanese Market. Institute for Monetary and Economic Studies, Bank of Japan.

[7]   De Dieu Ntawihebasenga, J., Mwita, P., & Mung’atu, J. (2014). Modelling the Volatility of Exchange Rates in Rwandese Markets. European Journal of Statistics and Probability, 2, 23-33.

[8]   De Sousa e Silva, J. et al. (2011). How to Deal with Extreme Observations in Empirical Finance: An Application to Capital Markets. Ph.D. Thesis, ISCTE Business School.

[9]   Embrechts, P., Klüppelberg, C., & Mikosch, T. (2013). Modelling Extremal Events: for Insurance and Finance (Vol. 33). Springer Science & Business Media.

[10]   Ergen, I. (2010). Var Prediction for Emerging Stock Markets: Garch Filtered Skewed t Distribution and GARCH Filtered EVT Method. Working Paper.

[11]   Ferreira, A., De Haan, L. et al. (2015). On the Block Maxima Method in Extreme Value theory: PWM Estimators. The Annals of Statistics, 43, 276-298.
https://doi.org/10.1214/14-AOS1280

[12]   Gencay, R., & Selcuk, F. (2004). Extreme Value Theory and Value-at-Risk: Relative Performance in Emerging Markets. International Journal of Forecasting, 20, 287-303.
https://doi.org/10.1016/j.ijforecast.2003.09.005

[13]   Gilli, M. et al. (2006). An Application of Extreme Value Theory for Measuring Financial Risk. Computational Economics, 27, 207-228.
https://doi.org/10.1007/s10614-006-9025-7

[14]   Kaberuka, D. et al. (2000). Rwanda Vision 2020. Republic of Rwanda Ministry of Finance and Economic Planning.

[15]   Longin, F. (2005). The Choice of the Distribution of Asset Returns: How Extreme Value Theory Can Help? Journal of Banking & Finance, 29, 1017-1035.
https://doi.org/10.1016/j.jbankfin.2004.08.011

[16]   Mahina, J. N., Muturi, W. M., & Memba, F. S. (2017). Influence of Loss Aversion Bias on Investments at the Rwanda Stock Exchange. International Journal of Accounting, Finance and Risk Management, 2, 131-137.

[17]   McNeil, A. J., & Saladin, T. (1997). The Peaks over Thresholds Method for Estimating High Quantiles of Loss Distributions. In Proceedings of 28th International ASTIN Colloquium (pp. 23-43).

[18]   Murenzi, R., Thomas, K., & Mung’atu, J. K. (2015) Modeling Exchange Market Volatility Risk in Rwanda Using Garch-EVT Approach. International Journal of Thesis Projects and Dissertations, 3, 67-80.

[19]   Mwamba, J. W. M., Hammoudeh, S., & Gupta, R. (2017). Financial Tail Risks in Conventional and Islamic Stock Markets: A Comparative Analysis. Pacific-Basin Finance Journal, 42, 60-82.
https://doi.org/10.1016/j.pacfin.2016.01.003

[20]   Nortey, E. N., Asare, K., & Mettle, F. O. (2015). Extreme Value Modelling of Ghana Stock Exchange Index. SpringerPlus, 4, Article No. 696.
https://doi.org/10.1186/s40064-015-1306-y

[21]   Oh, S. (2015). Multiple Imputation on Missing Values in Time Series Data. Ph.D. Thesis, Duke University.

[22]   Ramadhani, F., Nurrohmah, S., & Novita, M. (2017). Extreme Value Theory (EVT) Application on Estimating the Distribution of Maxima. In AIP Conference Proceedings (Vol. 1862, Article ID: 030156). AIP Publishing LLC.
https://doi.org/10.1063/1.4991260

[23]   Seymour, A. J., & Polakow, D. A. (2003). A Coupling of Extreme-Value Theory and Volatility Updating with Value-at-Risk Estimation in Emerging Markets: A South African Test. Multinational Finance Journal, 7, 3-23.

[24]   Tolikas, K., & Brown, R. A. (2006). The Distribution of the Extreme Daily Share Returns in the Athens Stock Exchange. European Journal of Finance, 12, 1-22.
https://doi.org/10.1080/1351847042000304107

[25]   Mauwa, J. et al (2017). Determinants of Financial Performance of Firms Listed on the Rwanda Stock Exchange. Doctoral Dissertation, COHRED, Jomo Kenyatta University of Agriculture and Technology.

 
 
Top