Modeling and Estimation of Market Risk Using Extreme Value Theory

Abstract

Most commercial airline agencies have suffered losses due to extreme conditions like climatic conditions, price fluctuations and airline problems. One of these airline agencies that have experienced large losses is the Kenya Airways. This study assesses the market risk in the Kenyan stock market using Kenya Airways (KQ) share prices.  This paper helps an investor to weigh whether to invest in the company at a particular time or not. Due to the fluctuations and variations of share prices, the Extreme Value Theory has been used to capture the extreme and rare events. Extreme Value Theory provides a well-established statistical model for the computation of extreme risk measures which include; Value at Risk and Expected Shortfall. In this paper, Univariate Extreme Value Theory is applied to model extreme prices of shares for the Kenya airways in Kenyan market. This paper demonstrates how successful Extreme value theory can be applied in predicting future Value at Risk to the share prices. This provides solutions to the problems faced by the investors and the owners of the commercial agency in the market. This paper concentrates on the Peak over Threshold (POT) as the method of estimating Value at Risk. This technique models the distribution of extremes and  the distribution of exceedances over a certain high threshold rather than the individual observations. It concentrates on observations that exceed central limits, focusing on the tail of the distribution. Extreme value theory is also applied to compute the tail risk measures at given confidence interval. An overview of the Extreme Value Theory and Peaks Over Threshold Method are also given. This paper also shows that POT is the best method since the modeling the exceedances, they follow a generalized pareto distribution (GPD) which fits the sample losses very well. This technique of extreme value theory helps us to model and estimate the stock market risk of the Kenya airways since it helps us to assess the goodness of fit of the series and detect the outliers and also in estimation of the extreme quantiles.This study used the stock data which was obtained from the Nairobi stock exchange (NSE). With Generalized Pareto Distribution the estimates of value at risk and the expected shortfall for share prices indicate that with probability 5% the daily loss for the stock market prices exceeds 2.5105%, for 1% the daily loss exceeds 2.5330, for 0.5% the daily loss exceeds 2.5358 and for 0.1% the daily  loss exceeds 2.5380%. These results can be used to estimate risk measures in the stock market as well as providing insights to the managers of the airline and also as a reference for actual or potential investors in the airline industry.

Keywords: Extreme Value Theory, Peak -Over Threshold (POT), Generalized Pareto Distribution (GPD), Value at Risk (VaR), Expected Shortfall (ES).