An Empirical Study for Comparison of Estimation Methods for Value at Risk, Tail Value at Risk, and Adjusted Tail Value at Risk Using Extreme Value Theory Approach to Stock Market Index

Sri Muslihah Bakhtiar(1*), Amran Amran(2), Khaeruddin Khaeruddin(3),

(1) Department Mathematics, FMIPA Universitas Hasanuddin
(2) Department Mathematics, FMIPA Universitas Hasanuddin
(3) Department Mathematics, FMIPA Universitas Hasanuddin
(*) Corresponding Author




DOI: https://doi.org/10.26858/jdm.v10i2.35702

Abstract


Risk management helps the financial industry to manage and estimate the risks that may occur by using risk measures. Financial series data mostly have a heavy tail distribution which causes the probability of extreme values to occur. To overcome these extreme values, it is necessary to apply a mathematical model in calculating risk estimates in financial data combined with the Extreme Value Theory approach. The Adjusted-TVaR model is a measure of the risk of modification of the TVaR model to eliminate outliers in the tail of the distribution. The purpose of this study is to measure the accuracy of the Value at Risk, Tail Value at Risk, and Adjusted Tail Value at Risk using the Peak Over Thresholdapproach in Extreme Value Theory Models.The results of the risk estimation research using the POT approach method, show that the higher the level of confidence and the chosen constant, the higher the value of Adj-TVaR presented. This value represents that the potential loss will be higher. The estimation results obtained that the VaR value is smaller than Adj-TVaR and Adj-TVaR is smaller than TVaR. This shows that Adj-TVaR is more efficient to use in terms of predicting risk value when compared to TVaR with the Peak Over Threshold approach


Keywords


Risk, Value at Risk, Tail Value at Risk, Adjusted TVaR, Extreme Value Theory, Peak Over Threshold.

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References


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