Abstract
Given the volatile nature of global financial markets, managing as well as predicting financial risk plays an increasingly important role in banking and finance. The Value at Risk (VaR) measure has emerged as the most prominent measure of downside market risk. It is measured as the alpha quantile of the profit and loss distribution. Recently a number of distributions have been proposed to model VaR: these include the extreme value theory distributions (EVT), Generalized Error Distribution (GED), Student’s t, and normal distribution. Furthermore, asymmetric as well as symmetric volatility models are combined with these distributions for out-sample VaR forecasts. This paper assesses the role of the distribution assumption and volatility specification in the accuracy of VaR estimates using daily closing prices of the Johannesburg Stock Exchange All Share Index (JSE ALSI). It is found that Student’s t distribution combined with asymmetric volatility models produces VaR estimates in out-sample periods that outperform those from models stemming from normal, EVT/symmetric volatility specification.
Highlights
The measurement of market risk has become a primary concern for market regulators and financial institutions
Contrary to many studies (Fernandez, 2003; Frey and McNeil, 2000) that recommend the use of extreme value theory distributions (EVT) to model the fat-tailed behaviour of return distributions in Value at Risk (VaR) computations, our results show that the Student’s t distribution combined with asymmetric volatility models produces VaR estimates in out-sample periods that outperform VaR estimates obtained with models stemming from normal, EVT/symmetric volatility specification
The volatility dynamics of financial returns are accurately modelled by employing the GARCH and/or Exponential GARCH (EGARCH) models proposed by Bollerslev (1986) and Nelson (1991) respectively
Summary
The measurement of market risk has become a primary concern for market regulators and financial institutions. The Capital Adequacy Directive by the Bank of International Settlement in Basel requires internationally active banks to hold sufficient risk capital to cover possible losses on their trading portfolios on 99% of occasions, over a holding period of ten days (Frey & McNeil, 2000). The value of such a capital requirement is termed VaR. VaR refers to the magnitude of likely losses over a specified period, resulting from ‘normal’ market movements
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