Extreme value modelling of Ghana stock exchange index

Abstract

Modelling of extreme events has always been of interest in fields such as hydrology and meteorology. However, after the recent global financial crises, appropriate models for modelling of such rare events leading to these crises have become quite essential in the finance and risk management fields. This paper models the extreme values of the Ghana stock exchange all-shares index (2000–2010) by applying the extreme value theory (EVT) to fit a model to the tails of the daily stock returns data. A conditional approach of the EVT was preferred and hence an ARMA-GARCH model was fitted to the data to correct for the effects of autocorrelation and conditional heteroscedastic terms present in the returns series, before the EVT method was applied. The Peak Over Threshold approach of the EVT, which fits a Generalized Pareto Distribution (GPD) model to excesses above a certain selected threshold, was employed. Maximum likelihood estimates of the model parameters were obtained and the model’s goodness of fit was assessed graphically using Q–Q, P–P and density plots. The findings indicate that the GPD provides an adequate fit to the data of excesses. The size of the extreme daily Ghanaian stock market movements were then computed using the value at risk and expected shortfall risk measures at some high quantiles, based on the fitted GPD model.

LES PREVISIONS STATIQUES ET DYNAMIQUES DES VALEURS A RISQUE (VaR) DES ACTIONS DE BANQUE : LE MODELE DE DEPASSEMENTS DE SEUIL (POT) ET LES MODELES DE SCORE AUTOREGRESSIFS GENERALISES (GAS)

“…Le backtesting des rendements quotidiens historiques prouve que ce modèle EVT conditionnel donne de bonnes prévisions pour tous les indices et tous les niveaux de confiance. Nortey et al (2015) modélise les valeurs extrêmes de l'indice des actions de la Bourse de Ghana (2000-2010) en appliquant la théorie de la valeur extrême (EVT) pour l'ajustement d'un modèle aux queues de la distribution des rendements quotidiens. Un modèle ARMA -GARCH a été ajusté aux données pour corriger les effets de l'autocorrélation et des termes hétéroscédastiques conditionnels présents dans la série de rendement, avant l'application d'EVT.…”

The Asymptotic Decision Scenarios of an Emerging Stock Exchange Market: Extreme Value Theory and Artificial Neural Network

“…Some economists performed traditional analysis using various econometric methods. For example, regime changes can occur, which means that these approaches are not beneficial for the prediction of investor decisions about the stock market (Enders 2004;Nortey et al 2015). The extreme value method can develop probability functions that can predict time-related data and study their nature as well as handle outliers.…”

“…Ghanaian general elections can have a detrimental impact on the stock market and hurt the performance of stocks due to the related market fluctuations. Additionally, regime change is a crucial factor that can impact investors' decision-making process (Nortey et al 2015). As (Farrid 2013) noted, a significant characteristic of the markets in African nations is the weak relationship between African stock markets and the principal stock exchanges around the world.…”

“…The findings of (Embrechts et al 2013) support the application of GEV distributions for modelling stocks in financial markets. In this context, these distributions are optimal distributions for extreme values in the conventional generalized autoregressive conditional heteroskedasticity (GARCH )procedure, which are generally followed by the returns on the market (Nortey et al 2015). The EVT model presented an improved fit to the ends of the GSE distribution, as the returns had a fat-tailed distribution that was asymmetric.…”

“…The fears for most financial analysts and risk administrators are that the events of abnormal market conditions produce enormous and unforeseen stock losses that could upset and likely leads to liquidations and absolute risk (Gavril 2009). A study by (Nortey et al 2015) revealed that general elections in Ghana usually threaten the stock performance, culminating in high volatility. A volatile stock market scares investors' self-confidence in the stock market.…”