scholarly journals The Quantitative Modeling of Operational Risk: Between G-and-H and EVT

2007 ◽  
Vol 37 (2) ◽  
pp. 265-291 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts ◽  
Dominik D. Lambrigger
Keyword(s):  
Value At Risk ◽  
Generalized Pareto Distribution ◽  
Operational Risk ◽  
Value Theory ◽  
Data Sets ◽  
Generalized Pareto ◽  
High Quantiles ◽  
Interesting Candidate ◽  
The One ◽  
Parameter Values

Operational risk has become an important risk component in the banking and insurance world. The availability of (few) reasonable data sets has given some authors the opportunity to analyze operational risk data and to propose different models for quantification. As proposed in Dutta and Perry [12], the parametric g-and-h distribution has recently emerged as an interesting candidate.In our paper, we discuss some fundamental properties of the g-and-h distribution and their link to extreme value theory (EVT). We show that for the g-and-h distribution, convergence of the excess distribution to the generalized Pareto distribution (GPD) is extremely slow and therefore quantile estimation using EVT may lead to inaccurate results if data are well modeled by a g-and-h distribution. We further discuss the subadditivity property of Value-at-Risk (VaR) for g-and-h random variables and show that for reasonable g and h parameter values, superadditivity may appear when estimating high quantiles. Finally, we look at the g-and-h distribution in the one-claim-causes-ruin paradigm.

scholarly journals The Quantitative Modeling of Operational Risk: Between G-and-H and EVT

2007 ◽  
Vol 37 (02) ◽  
pp. 265-291 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts ◽  
Dominik D. Lambrigger
Keyword(s):  
Value At Risk ◽  
Generalized Pareto Distribution ◽  
Operational Risk ◽  
Value Theory ◽  
Data Sets ◽  
Generalized Pareto ◽  
High Quantiles ◽  
Interesting Candidate ◽  
The One ◽  
Parameter Values

Operational risk has become an important risk component in the banking and insurance world. The availability of (few) reasonable data sets has given some authors the opportunity to analyze operational risk data and to propose different models for quantification. As proposed in Dutta and Perry [12], the parametric g-and-h distribution has recently emerged as an interesting candidate. In our paper, we discuss some fundamental properties of the g-and-h distribution and their link to extreme value theory (EVT). We show that for the g-and-h distribution, convergence of the excess distribution to the generalized Pareto distribution (GPD) is extremely slow and therefore quantile estimation using EVT may lead to inaccurate results if data are well modeled by a g-and-h distribution. We further discuss the subadditivity property of Value-at-Risk (VaR) for g-and-h random variables and show that for reasonable g and h parameter values, superadditivity may appear when estimating high quantiles. Finally, we look at the g-and-h distribution in the one-claim-causes-ruin paradigm.

Using Extreme Value Theory to Model Electricity Price Risk with an Application to the Alberta Power Market

2005 ◽  
Vol 23 (5) ◽  
pp. 375-403 ◽  
Author(s):  
W. D. Walls ◽  
Wei. Zhang
Keyword(s):  
Extreme Value Theory ◽  
Value At Risk ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Financial Assets ◽  
Historical Simulation ◽  
Generalized Pareto ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

Value-at-risk (VaR) is a measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR has become a standard measure of market risk and a common practice is to compute VaR by assuming that changes in value of the portfolio are conditionally normally distributed. However, assets returns usually come from heavy-tailed distributions, so computing VaR under the assumption of conditional normality can be an important source of error. We illustrate in our application to competitive electric power prices in Alberta, Canada, that VaR estimates based on extreme value theory models, in particular the generalized Pareto distribution are, more accurate than those produced by alternative models such as normality or historical simulation.

scholarly journals STRATEGI PENANGANAN RISIKO OPERASIONAL PEMASARAN PRODUK TEH CELUP HIJAU WALINI PADA INDUSTRI HILIR TEH PT PERKEBUNAN NUSANTARA VIII, BANDUNG, JAWA BARAT

2019 ◽  
Vol 11 (2) ◽  
pp. 100-115
Author(s):  
Idzhar Jaya Nugraha ◽  
Akhmad Riyadi Wastra ◽  
Lilis Imamah Ichdayati
Keyword(s):  
Green Tea ◽  
Value At Risk ◽  
Operational Risk ◽  
International Market ◽  
Mitigation Strategy ◽  
Z Score ◽  
Is Strategy ◽  
Plantation Company ◽  
The One ◽  
Brand Product

Tea is an Indonesian excellent product that has been recognized worldwide. Indonesia is the seventh best tea producer which have international market potential.Therefore Tea Indonesia is expected to take advantage on existing opportunities from downstream industry of tea. The one of stated-owned plantation company who have downstream industry of tea is PT Perkebunan Nusantara VIII. Walini’s tea is a one famous brand product for this company. The development downstream industry of tea PTPN VIII is faced with yet achieved the expected sales. Amount of cost operational marketing and sales are indicated of operational risk. The objective of this study is strategy handling of marketing operational risk Walini Green tea bag product in downstream industry of tea PTPN VIII. Identification risk is first step to know the problem of marketing operational in downstream industry of tea PTPN VIII. By using Z-Score and Value at Risk (VAR) metode, it be showed the result of probability and impact of marketing operational risk. Preventif and mitigation strategy can be handling this company to growth up the expected sales.

scholarly journals Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory

1997 ◽  
Vol 27 (1) ◽  
pp. 117-137 ◽  
Author(s):  
Alexander J. McNeil
Keyword(s):  
Extreme Value Theory ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Parametric Curve ◽  
Excess Loss ◽  
Generalized Pareto ◽  
Fire Insurance ◽  
Loss Severity ◽  
Parametric Curve Fitting

AbstractGood estimates for the tails of loss severity distributions are essential for pricing or positioning high-excess loss layers in reinsurance. We describe parametric curve-fitting methods for modelling extreme historical losses. These methods revolve around the generalized Pareto distribution and are supported by extreme value theory. We summarize relevant theoretical results and provide an extensive example of their application to Danish data on large fire insurance losses.

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.

A PIECEWISE-DEFINED SEVERITY DISTRIBUTION-BASED LOSS DISTRIBUTION APPROACH TO ESTIMATE OPERATIONAL RISK: EVIDENCE FROM CHINESE NATIONAL COMMERCIAL BANKS

2009 ◽  
Vol 08 (04) ◽  
pp. 727-747 ◽  
Author(s):  
JIANPING LI ◽  
JICHUANG FENG ◽  
JIANMING CHEN
Keyword(s):  
Commercial Banks ◽  
Public Information ◽  
Generalized Pareto Distribution ◽  
Operational Risk ◽  
Regulatory Capital ◽  
Loss Distribution ◽  
Generalized Pareto ◽  
Loss Distribution Approach ◽  
Indicator Approach ◽  
International Banks

Following the Basel II Accord, with the increased focus on operational risk as an aspect distinct from credit and market risk, quantification of operational risk has been a major challenge for banks. This paper analyzes implications of the advanced measurement approach to estimate the operational risk. When modeling the severity of losses in a realistic manner, our preliminary tests indicate that classic distributions are unable to fit the entire range of operational risk data samples (collected from public information sources) well. Then, we propose a piecewise-defined severity distribution (PSD) that combines a parameter form for ordinary losses and a generalized Pareto distribution (GPD) for large losses, and estimate operational risk by the loss distribution approach (LDA) with Monte Carlo simulation. We compare the operational risk measured with piecewise-defined severity distribution based LDA (PSD-LDA) with those obtained from the basic indicator approach (BIA), and the ratios of operational risk regulatory capital of some major international banks with those of Chinese commercial banks. The empirical results reveal the rationality and promise of application of the PSD-LDA for Chinese national commercial banks.

scholarly journals ON THE TWO STEP THRESHOLD SELECTION FOR OVER-THRESHOLD MODELLING

2012 ◽  
Vol 1 (33) ◽  
pp. 42
Author(s):  
Pietro Bernardara ◽  
Franck Mazas ◽  
Jérôme Weiss ◽  
Marc Andreewsky ◽  
Xavier Kergadallan ◽  
...  
Keyword(s):  
Pareto Distribution ◽  
Extreme Values ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Water Levels ◽  
Distributed Data ◽  
Threshold Selection ◽  
The Past ◽  
Generalized Pareto ◽  
Selection For

In the general framework of over-threshold modelling (OTM) for estimating extreme values of met-ocean variables, such as waves, surges or water levels, the threshold selection logically requires two steps: the physical declustering of time series of the variable in order to obtain samples of independent and identically distributed data then the application of the extreme value theory, which predicts the convergence of the upper part of the sample toward the Generalized Pareto Distribution. These two steps were often merged and confused in the past. A clear framework for distinguishing them is presented here. A review of the methods available in literature to carry out these two steps is given here together with the illustration of two simple and practical examples.

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