Capturing Tail Risks Beyond VaR

2012 ◽  
Vol 15 (03) ◽  
pp. 1250015 ◽  
Author(s):  
Woon Kong Wong ◽  
Guobin Fan ◽  
Yong Zeng
Keyword(s):  
Financial Markets ◽  
Value At Risk ◽  
Pareto Distribution ◽  
Risk Measures ◽  
Generalized Pareto Distribution ◽  
Small Sample ◽  
Generalized Pareto ◽  
Distribution Tail ◽  
Data History ◽  
Average Loss

Since Value-at-Risk (VaR) disregards tail losses beyond the VaR boundary, the expected shortfall (ES), which measures the average loss when a VaR is exceeded, and the tail-risk-of-VaR (TR), which sums the sizes of tail losses, are used to investigate risks at the tails of distributions for major stock markets. As VaR exceptions are rare, we employ the saddlepoint or small sample asymptotic technique to backtest ES and TR. Because the two risk measures are complementary to each other and hence provide more powerful backtests, we are able to show that (a) the correct specification of distribution tail, rather than heteroscedastic process, plays a key role to accurate risk forecasts; and (b) it is best to model the tails separately from the central part of distribution using the Generalized Pareto Distribution (GPD). To sum up, we provide empirical evidence that financial markets behave differently during crises, and extreme risks cannot be modeled effectively under normal market conditions or based on a short data history.

scholarly journals Testes para avaliação das previsões de value-at-risk e expected shortfall

2019 ◽  
Vol 17 (4) ◽  
pp. 56
Author(s):  
Jaime Enrique Lincovil ◽  
Chang Chiann
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Pareto Distribution ◽  
Risk Measures ◽  
Generalized Pareto Distribution ◽  
Expected Shortfall ◽  
Empirical Power ◽  
Test Procedures ◽  
Generalized Pareto ◽  
Evaluating Forecasts

<p>Evaluating forecasts of risk measures, such as value–at–risk (VaR) and expected shortfall (ES), is an important process for financial institutions. Backtesting procedures were introduced to assess the efficiency of these forecasts. In this paper, we compare the empirical power of new classes of backtesting, for VaR and ES, from the statistical literature. Further, we employ these procedures to evaluate the efficiency of the forecasts generated by both the Historical Simulation method and two methods based on the Generalized Pareto Distribution. To evaluate VaR forecasts, the empirical power of the Geometric–VaR class of backtesting was, in general, higher than that of other tests in the simulated scenarios. This supports the advantages of using defined time periods and covariates in the test procedures. On the other hand, to evaluate ES forecasts, backtesting methods based on the conditional distribution of returns to the VaR performed well with large sample sizes. Additionally, we show that the method based on the generalized Pareto distribution using durations and covariates has optimal performance in forecasts of VaR and ES, according to backtesting.</p>

scholarly journals Quantile estimation for the generalized pareto distribution with application to finance

2012 ◽  
Vol 22 (2) ◽  
pp. 297-311 ◽  
Author(s):  
Jelena Jockovic
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Quantile Estimation ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

Generalized Pareto distributions (GPD) are widely used for modeling excesses over high thresholds (within the framework of the POT-approach to modeling extremes). The aim of the paper is to give the review of the classical techniques for estimating GPD quantiles, and to apply these methods in finance - to estimate the Value-at-Risk (VaR) parameter, and discuss certain difficulties related to this subject.

scholarly journals A New Parameter Estimator for the Generalized Pareto Distribution under the Peaks over Threshold Framework

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 406 ◽  
Author(s):  
Xu Zhao ◽  
Zhongxian Zhang ◽  
Weihu Cheng ◽  
Pengyue Zhang
Keyword(s):  
Value At Risk ◽  
Environmental Science ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
High Threshold ◽  
Threshold Selection ◽  
Peaks Over Threshold ◽  
Scale Parameters ◽  
Generalized Pareto ◽  
Critical Issues

Techniques used to analyze exceedances over a high threshold are in great demand for research in economics, environmental science, and other fields. The generalized Pareto distribution (GPD) has been widely used to fit observations exceeding the tail threshold in the peaks over threshold (POT) framework. Parameter estimation and threshold selection are two critical issues for threshold-based GPD inference. In this work, we propose a new GPD-based estimation approach by combining the method of moments and likelihood moment techniques based on the least squares concept, in which the shape and scale parameters of the GPD can be simultaneously estimated. To analyze extreme data, the proposed approach estimates the parameters by minimizing the sum of squared deviations between the theoretical GPD function and its expectation. Additionally, we introduce a recently developed stopping rule to choose the suitable threshold above which the GPD asymptotically fits the exceedances. Simulation studies show that the proposed approach performs better or similar to existing approaches, in terms of bias and the mean square error, in estimating the shape parameter. In addition, the performance of three threshold selection procedures is assessed by estimating the value-at-risk (VaR) of the GPD. Finally, we illustrate the utilization of the proposed method by analyzing air pollution data. In this analysis, we also provide a detailed guide regarding threshold selection.

scholarly journals GENERALIZED PARETO DISTRIBUTION UNTUK PENGUKURAN VALUE AT RISK PADA PORTOFOLIO SAHAM SYARIAH DAN APLIKASINYA MENGGUNAKAN GUI MATLAB

2018 ◽  
Vol 7 (3) ◽  
pp. 224-235
Author(s):  
Desi Nur Rahma ◽  
Di Asih I Maruddani ◽  
Tarno Tarno
Keyword(s):  
At Risk ◽  
Capital Market ◽  
Value At Risk ◽  
Pareto Distribution ◽  
Extreme Values ◽  
Generalized Pareto Distribution ◽  
Generalized Pareto ◽  
Heavy Tailed ◽  
Is Value

The capital market is one of long-term investment alternative. One of the traded products is stock, including sharia stock. The risk measurement is an important thing for investor in other that can decrease investment loss. One of the popular methods now is Value at Risk (VaR). There are many financial data that have heavy tailed, because of extreme values, so Value at Risk Generalized Pareto Distribution is used for this case. This research also result a Matlab GUI programming application that can help users to measure the VaR. The purpose of this research is to analyze VaR with GPD approach with GUI Matlab for helping the computation in sharia stock. The data that is used in this case are PT XL Axiata Tbk, PT Waskita Karya (Persero) Tbk, dan PT Charoen Pokphand Indonesia Tbk on January, 2nd 2017 until May, 31st 2017. The results of VaRGPD are: EXCL single stock VaR 8,76% of investment, WSKT single stock VaR 4% of investment, CPIN single stock VaR 5,86% of investment, 2 assets portfolio (EXCL and WSKT) 4,09% of investment, 2 assets portfolio (EXCL and CPIN) 5,28% of investment, 2 assets portfolio (WSKT and CPIN) 3,68% of investment, and 3 assets portfolio (EXCL, WSKT, and CPIN) 3,75% of investment. It can be concluded that the portfolios more and more, the risk is smaller. It is because the possibility of all stocks of the company dropped together is small. Keywords: Generalized Pareto Distribution, Value at Risk, Graphical User Interface, sharia stock

scholarly journals Modeling of Extreme Crude Oil Price using the Generalized Pareto Distribution: Brent and West Texas Benchmark Price

2021 ◽  
pp. 359-374
Author(s):  
Ngozi J. Amachukwu ◽  
Happiness O. Obiora-Ilouno ◽  
Edwin I. Obisue
Keyword(s):  
At Risk ◽  
Crude Oil ◽  
Value At Risk ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Expected Shortfall ◽  
Oil Price ◽  
Crude Oil Price ◽  
Generalized Pareto ◽  
West Texas

Background and objective: Crude oil is an essential commodity in many countries of the world. This work studies the risk involved in the extreme crude oil price, using the daily crude oil price of the Brent and the West Texas benchmark from year 1990 to 2019. Materials and methods: The Peak Over Threshold (POT) approach of the Generalized Pareto Distribution (GPD) was used to model the extreme crude oil price while the value at risk and the expected shortfall was used to quantify the risk involved in extreme price of crude oil. The GPD, using the Q-Q plot was found to be a good model for the extreme values of the crude oil price. Results: The Value at Risk (VaR) and the Expected Shortfall (ES) calculated at 90%, 95% and 99% with the Maximum Likelihood estimators of GPD parameters and the threshold values were found to decrease with increase in quantile for both benchmark. This shows that risk involved in extreme crude oil price will be borne only by the investors and public. Conclusion: It was also found that the VaR and ES of the Brent are higher than that of West Texas. This implies that it is safer to invest in West Texas crude oil.

scholarly journals On estimation of loss distributions and risk measures

2012 ◽  
Vol 16 (1) ◽  
pp. 53-67
Author(s):  
Meelis Käärik ◽  
Anastassia Žegulova
Keyword(s):  
Pareto Distribution ◽  
Risk Measures ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Third Party ◽  
Insurance Fund ◽  
Parameter Estimates ◽  
Generalized Pareto ◽  
Wide Range ◽  
Heavy Tailed

The estimation of certain loss distribution and analyzing its properties is a key issue in several finance mathematical and actuarial applications. It is common to apply the tools of extreme value theory and generalized Pareto distribution in problems related to heavy-tailed data. Our main goal is to study third party liability claims data obtained from Estonian Traffic Insurance Fund (ETIF). The data is quite typical for insurance claims containing very many observations and being heavy-tailed. In our approach the fitting consists of two parts: for main part of the distribution we use lognormal fit (which was the most suitable based on our previous studies) and a generalized Pareto distribution is used for the tail. Main emphasis of the fitting techniques is on the proper threshold selection. We seek for stability of parameter estimates and study the behaviour of risk measures at a wide range of thresholds. Two related lemmas will be proved.

scholarly journals PENILAIAN VALUE AT RISK DENGAN PENDEKATAN EXTREME VALUE THEORYDAN GENERALIZED PARETO DISTRIBUTION STUDI KASUS BANK BUMN DI INDONESIA PADA PERIODE TAHUN 2008-2018

2019 ◽  
Vol 13 (1) ◽  
pp. 63-72
Author(s):  
Yanur Akhmadi ◽  
Iqbal Mustofa ◽  
Hotmauly Media Rika ◽  
Dewi Hanggraeni
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Extreme Value ◽  
Generalized Pareto

Perkembangan sektor perbankan di Indonesia dalam 10 tahun mengalami pertumbuhan yang agresif, tetapi juga memperhatikan rasio modal berdasarkan risiko sesuai dengan ketentuan otoritas. Bank BUMN di Indonesia menguasasi ?45% dari total aset pada sektor perbankan, dan memiliki rasio penyediaan modal minimum yang lebih tinggi dari yang disyaratkan otoritas. Penelitian in imembahas perhitungan VaR dengan metode GEV dan GPD, serta membandingkannya dengan rasio penyediaan modal minimum bank. Hasil perhitungan dengan menggunakan metode GPD paling mendekati nilai rasio modal bank, selain itu kedua hasil perhitungan baik GEV dan GPD lebih tinggi saat dibandingkan dengan perhitungan VaR dengan metode lainnya ataupun ketentuan yang ditetapkan oleh otoritas.

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