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• W3124813585 abstract "ABSTRACTThe aim of this paper is to derive a coherent risk measure for heavy tailed GARCH processes using extreme value theory. For the proposed measure, the risk associated to a given portfolio is less than the sum of the stand-alone risks of its components. This measure which is value at risk (VaR), is the limiting result of an infinity shift of location and is less sensitive with respect to location change. Based on two international stock markets applications and an empirical backtesting procedure, the proposed VaR is found to be more accurate in all quantile levels.JEL: C22, C58, G15KEYWORDS: Risk Management, Extreme Value Theory, Non-linear Models, Backtesting, Stock Market Index(ProQuest: ... denotes formulae omitted.)INTRODUCTIONSEveral authors argue Value at Risk (VaR) is the best integrated risk management tool in both financial and insurance studies. VaR is defined as an amount lost in a portfolio with a given small probability over a fixed number of days. Besides its simplicity and intuitive interpretation, VaR works across different asset classes such as stocks and bonds. However, this tool has numerous shortcomings. First, for several high frequency time series data characterized by thick-tail, such as stock returns, if the data are still supposed following normal distribution, the VaR would be underestimated. Second, the normal distribution hypothesis is always rejected by Jarque-Bera test in empirical analysis. Therefore, how to deal with these two limitations is paramount in risk management. In order to avoid these two first shortcomings, one possible solution is based on non-parametric methods that make no assumptions concerning the nature of the empirical distribution function. The third VaR drawback is the stylized fact namely heterocedasticity phenomena that describe financial data. The latter often exhibit volatility clustering or persistence. In volatility clustering, large changes tend to follow large changes, and small changes tend to follow small changes. To explain these features of the data, Bollerslev (1986) proposed the popular GARCH models. The latter takes into account volatility clustering and excess kurtosis (fat tail behavior) which are considered as the forth VaR shortcoming. To overcome the problem of fat tail behavior, one can use extreme value theory (EVT). This theory is an interesting tool to deal with extreme observations in order to measure the density in the tail. Combining with GARCH model, EVT has the different statistical characteristics to describe the performance of the tick-tail properties of the high frequency financial time series data.The remainder sections are organized as follows. Section 2 outlines VaR concept based on EVT as proposed by Dekkers et al.(1989). The proposed modified VaR is introduced in Section 3. Backtesting procedure is outlined in section 4. In Section 5, the proposed method is illustrated through a real case study and backtesting methodologies. Finally, conclusion is provided in section 6.LITERATURE REVIEWThere is a growing literature on application of EVT approaches to estimate VaR. In series of articles, McNeil (1997, 1998, and 1999) proposed to use the tail index in order to estimate VaR for the financial time series using EVT. Silva and Mendes (2003) show that VaR estimation based on EVT is more conservative to determine capital requirements than traditional methods. Using daily returns, Gencay et al. (2003) indicate that GARCH and generalized Pareto distribution (GPD) models are more preferable than several others traditional models for most quantile levels. Maghyereh and Al-Zoubi (2006) investigate performances of some models to estimate VaR in seven Middle East and North Africa (MENA) countries. They outline that EVT models perform better in five of the MENA stock markets. Alper et al. (2007) compare the performance of eight filtered EVT models with those of GARCH and FIGARCH models. …" @default.
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• W3124813585 date "2014-05-01" @default.
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• W3124813585 title "Value at Risk Estimation for Heavy Tailed Distributions" @default.
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