Application of extreme value theory in the estimation of value at risk in Kenyan stock market

Abstract

Most financial institutions have faced a lot of losses due to the fluctuations of commodities prices. Traditionally normal distribution was applied and could not capture rare events which caused enormous losses. The objective is to estimate conditional quantiles of the returns of an asset which leads to Value at Risk directly using Extreme Value Theory which estimates the tails of the innovation distribution of financial returns. One of the most important approaches to risk management used in this study is quantification of risk using Value at Risk (VaR) which is achieved by Extreme Value Theory (EVT) that have the ability to estimate observations beyond the range of the data or out-of-sample data (extreme quantiles). Data from Nairobi Stock Exchange (NSE) specifically equities from Barclays Bank was applied at different confidence levels and it was observed that Peak-Over Threshold( POT) model of EVT and Generalized Pareto Distribution( GPD) which describes the tail of the financial returns captures the rare events which makes it the most robust method of estimating VaR.