VAR and ES calculation based on the Extreme Value Theory (block maxima and GPD): Evidence from Tehran Stock Exchange (TSE)
Subject Areas : Financial engineeringMansour Kashi 1 , S. Hassan Hoseini 2 , mohammad Mousa Ghaliliou 3 , saeed Golkarian Arani 4
1 - Master of Science in Finance and Documentation
2 - Ph.D. student and faculty member of Imam Ali University, Tehran, Iran
3 - Master student of Payame Noor University, Tehran, Iran
4 - Master Student, Islamic Azad University, Science and Research Branch, Tehran, Iran
Keywords: Value at risk, Extreme Value Theory, Expected Shortfall, Generalized Pareto distribution,
Abstract :
Current study, has explores the VAR and ES in the Tehran Stock Exchange (TSE) by using the Extreme Value Theory (block maxima and GPD). Earlier estimates of the preliminary findings of the analysis that uses statistics, Empirical Distribution Function, Mean Excess Function and QQ plot, Pareto and heavy-tailed behavior were found data. To estimate the optimal threshold value, we have Mean Excess Function and hill plot applied. To estimate the optimal threshold value, Mean Excess Function and Hill plot use the statistics mentioned for the positive and negative returns, the threshold value for GPD models are about ./75 And ./60 have provided. Comparing the estimated residual value model classic extreme (monthly, quarterly, six month and one year) and the GPD, concluded the optimal performance GPD calculated on the value of extreme block which is highly sensitive to the choice of the period. Finally, to estimate VAR and ES, we GPD model demonstrated that a better performance was applied. The results showed that VAR and ES should not be the dominant financial risk management. In other words, dependence on individual risk scale for ignoring the problem will create portfolio risk information. So to contain the missing information by VAR and ES, it is essential that the various aspects of the distribution of losses / profits look like heavy-tailed.
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