scholarly journals EVT-based estimation of risk capital and convergence of high quantiles

2008 ◽  
Vol 40 (03) ◽  
pp. 696-715 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts
Keyword(s):  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Second Order ◽  
Parametric Models ◽  
Tail Behavior ◽  
Parametric Approach ◽  
Risk Capital ◽  
High Quantiles ◽  
Estimation Of Risk

We discuss some issues regarding the accuracy of a quantile-based estimation of risk capital. In this context, extreme value theory (EVT) emerges naturally. The paper sheds some further light on the ongoing discussion concerning the use of a semi-parametric approach like EVT and the use of specific parametric models such as the g-and-h. In particular, we discusses problems and pitfalls evolving from such parametric models when using EVT and highlight the importance of the underlying second-order tail behavior.

scholarly journals EVT-based estimation of risk capital and convergence of high quantiles

2008 ◽  
Vol 40 (3) ◽  
pp. 696-715 ◽  
Author(s):  
Matthias Degen ◽  
Paul Embrechts
Keyword(s):  
Extreme Value Theory ◽  
Value Theory ◽  
Extreme Value ◽  
Second Order ◽  
Parametric Models ◽  
Tail Behavior ◽  
Parametric Approach ◽  
Risk Capital ◽  
High Quantiles ◽  
Estimation Of Risk

We discuss some issues regarding the accuracy of a quantile-based estimation of risk capital. In this context, extreme value theory (EVT) emerges naturally. The paper sheds some further light on the ongoing discussion concerning the use of a semi-parametric approach like EVT and the use of specific parametric models such as the g-and-h. In particular, we discusses problems and pitfalls evolving from such parametric models when using EVT and highlight the importance of the underlying second-order tail behavior.

scholarly journals Generalized regular variation of second order

1996 ◽  
Vol 61 (3) ◽  
pp. 381-395 ◽  
Author(s):  
Laurens de Haan ◽  
Ulrich Stadtmüller
Keyword(s):  
Asymptotic Behaviour ◽  
Extreme Value Theory ◽  
Regular Variation ◽  
Inverse Function ◽  
Limit Relation ◽  
Laplace Transforms ◽  
Auxiliary Function ◽  
Value Theory ◽  
Extreme Value ◽  
Second Order

AbstractAssume that for a measurable funcion f on (0, ∞) there exist a positive auxiliary function a(t) and some γ ∈ R such that . Then f is said to be of generalized regular variation. In order to control the asymptotic behaviour of certain estimators for distributions in extreme value theory we are led to study regular variation of second order, that is, we assume that exists non-trivially with a second auxiliary function a1(t). We study the possible limit functions in this limit relation (defining generalized regular variation of second order) and their domains of attraction. Furthermore we give the corresponding relation for the inverse function of a monotone f with the stated property. Finally, we present an Abel-Tauber theorem relating these functions and their Laplace transforms.

A Handbook of Second Order Expansions of Quantile Functions and Asymptotic Record Values Laws

2021 ◽  
Author(s):  
Gane Samb Lo ◽  
Moumouni Diallo ◽  
Modou Ngom
Keyword(s):  
Extreme Value Theory ◽  
Domain Of Attraction ◽  
Rates Of Convergence ◽  
Record Values ◽  
Value Theory ◽  
Extreme Value ◽  
Second Order ◽  
Record Value ◽  
Quantile Functions ◽  
The Right

In this monograph, our final objective is to provide second order expansions of quantile functions of as many probability laws as possible. Second order expansions of quantile functions are important tools for finding extreme value domain of attraction of probability laws and for discovering rates of convergence in extreme value theory. We hope that readers will make profit of the results in their works by using the right expansions of quantile functions from the monograph. In that spirit, we apply the quantiles expansions exposed here to deliver the corresponding asymptotic laws of records values. <br><br> In this first edition, fifty four distributions are concerned. For each of those probability laws, full computations for finding the expansion and the asymptotic record value theory are entirely justified. We will regularly update the handbook by adding probability laws in later editions.

scholarly journals Extreme Value Theory and Auction Models

2021 ◽  
Vol 16 (2) ◽  
pp. 1-15
Author(s):  
Paolo Riccardo Morganti
Keyword(s):  
Extreme Value Theory ◽  
Practical Interest ◽  
Value Theory ◽  
Extreme Value ◽  
Parametric Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Nonparametric Estimators ◽  
Transaction Prices ◽  
Auction Models

The objective of this article is to develop a parametric approach to estimating auctions with incomplete data using Extreme Value Theory (EVT). The methodology is mainly theoretical: we first review that, when only transaction prices can be observed, the distribution of private valuations is irregularly identified. The sample bias produced by nonparametric estimators will affect all functionals of practical interest. We provide simulations for a best-case scenario and a worst-case scenario. Our results show that, compared to nonparametric approaches, the approximation of such functionals developed using EVT produces more accurate results, is easy to compute, and does not require strong assumptions about the unobserved distribution of bidders' valuations. It is recommended that financial operators working with auctions use this parametric approach when facing incomplete datasets. Given the difficult nature of the analysis, this work does not provide large sample properties for the proposed estimators and recommends the use of bootstrapping. This article contributes originally to the literature of structural estimation of auction models providing a useful and robust parametric approximation.

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