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.
Highlights
Extreme Value Distribution has come forth as one of the most significant probability theories for social and applied sciences
In 1990s, due to the currency crisis and sub-primes in 2007, stock market crashes and credit default, a research study by (Gilli et al, 2006) showed the potential of Extreme Value Theory (EVT) approach in finance and illustrated EVT using Block Maxima Method (BMM) and Peak Over Threshold (POT) in modelling Value at Risk (VaR), Expected Shortfalls (ES) and return level. His outcome depicted that POT was considered to be more efficient in modelling limited data and not depending on the requirement for large data set as BMM because it exploits better information in sampling (Murenzi et al, 2015). both returns and residuals have fat tail behaviour and concluded that GARCH-EVT approach can be worked very well
The main focus is on using Block Maxima method, Peak over Threshold, Value at Risk, and Expected Shortfall to model the stocks returns
Summary
Extreme Value Distribution has come forth as one of the most significant probability theories for social and applied sciences. In 1990s, due to the currency crisis and sub-primes in 2007, stock market crashes and credit default, a research study by (Gilli et al, 2006) showed the potential of EVT approach in finance and illustrated EVT using Block Maxima Method (BMM) and Peak Over Threshold (POT) in modelling VaR, ES and return level. Another study on volatility analysis of exchange rate of emerging economies: a case of East Africa community showed that the existence of high rates of exchange volatility could be explained by the fact that these currencies are not pegged to any major international currency (Silva et al, 2011) Another illustration is a paper from (Tolikas & Brown, 2006) where the authors used the Extreme Value Theory (EVT) to research the asymptotic distribution of the lower tail of daily returns in the Athens Stock Exchange (ASE) over the period 1986 to 2001.
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