On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles

Chen, James Ming

doi:10.2139/ssrn.3136278

Cited by 19 publications

(13 citation statements)

References 121 publications

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“…VaR describes the maximum possible loss over a given time interval, with a given confidence level e.g. Chen [4]. One may say that VaR is a critical value of loss distribution before it reaches the worst risk.…”

Section: Risk Measure-based Risk Allocation Value-at-risk and Its Extmentioning

confidence: 99%

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Aggregate Risk Model and Risk Measure-Based Risk Allocation

Syuhada

2020

InPrime:Ind.Jour.Pure.Applied.Math

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In actuarial modeling, aggregate risk is known as more attractive rather than individual risk. It has, however, usual difficulty in finding (the exact form of) joint probability distribution. This paper considers aggregate risk model and employ translated gamma approximation to handle such distribution function formulation. In addition, we deal with the problem of risk allocation in such model. We compute in particular risk allocation based on risk measure forecasts of Value-at-Risk (VaR) and its extensions: improved VaR and Tail VaR. Risk allocation shows the contribution of each individual risk to the aggregate. It has a constraint that the risk measure of aggregate risk is equal to the aggregate of risk measure of individual risk.Keywords: allocation methods; tail-value-at-risk; translated gamma approximation. AbstrakRisiko agregat merupakan kajian yang lebih menarik dalam pemodelan aktuaria, dibandingkan dengan risiko individu. Namun fungsi distribusi risiko agregat sulit ditentukan bentuk eksaknya. Artikel ini membahas mengenai model risiko agregat dan menggunakan metode aproksimasi Translasi Gamma untuk menentukan fungsi distribusi risiko agregat. Berdasarkan fungsi distribusi tersebut, dapat diprediksi alokasi risiko agregat. Metode alokasi risiko agregat diterapkan pada ukuran risiko Value-at-Risk (VaR) dan pengembangannya: improved VaR dan Tail-VaR. Alokasi risiko menyatakan nilai kontribusi setiap risiko individu terhadap ukuran risiko agregat. Jumlahan atau agregat dari setiap alokasi risiko individu sama dengan ukuran risiko agregat.Kata kunci: aproksimasi Translasi Gamma; alokasi risiko; Tail-Value-at-Risk.

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Section: Risk Measure-based Risk Allocation Value-at-risk and Its Extmentioning

confidence: 99%

“…It reflects the maximum tolerated risk at certain confidence level and time period, e.g. Nieto and Ruiz [3], for latest review on VaR and its backtesting, and Chen [4]. VaR generally tell us a warning before the worse risk occurs as well as a preparation of capital.…”

Section: Introductionmentioning

confidence: 99%

Aggregate Risk Model and Risk Measure-Based Risk Allocation

Syuhada

2020

InPrime:Ind.Jour.Pure.Applied.Math

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“…Otros trabajos relevantes recientes sobre expectiles como medida del riesgo financiero y relacionados con el backtesting son: Bellini y Bignozzi (2015) y Nolde y Ziegel (2017). Chen (2018) es el mejor y más completo review hasta el momento.…”

Section: Expectilesunclassified

Evolución de la medición del riesgo financiero en los últimos 40 años: una panorámica con especial mención en la banca

Vaca

López²

2019

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El objetivo de este artículo es ofrecer una panorámica de la evolución de la medición y gestión del riesgo financiero en los últimos 40 años, con especial mención a la banca. Tras una etapa basada en los principios de la Modern Portfolio Theory (MPT), hace 25 años se produce una revolución con la introducción del Value-at-Risk (VaR). Desde entonces, la introducción de nuevas medidas cuantitativas, con complejidad matemática creciente, no se ha detenido, en una interacción continua entre académicos, profesionales y reguladores, como respuesta a las sucesivas crisis financieras y bancarias. Entre ellas, destacan las medidas coherentes del riesgo (concretamente el Expected Shortfall), espectrales y basadas en expectiles. Se concluye que el VaR y el Expected Shortfall (ES) continúan siendo, a pesar de sus limitaciones, las dos medidas más utilizadas tanto desde el punto de vista interno de los bancos, como por parte del regulador y supervisor de su solvencia. Finalmente, se plantean algunas de las líneas de investigación en este campo que tratan de abordar los retos en el futuro de la medición del riesgo financiero en banca.

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“…Widely used in insurance and statistics, it has recently gained some interest in finance as it bears some interesting features for the assessment of tail risk in comparison to the industry wide expected shortfall risk measure introduced by Artzner et al [4]. From its definition, expectile is elicitable, which is a useful property in terms of backtesting, see Gneiting [17], Ziegel [35], Bellini and Bignozzi [6], Emmer et al [14], and Chen [10] for a discussion about the financial relevance. In the seminal paper Weber [33], and later Ziegel [35], Bellini and Bignozzi [6], Delbaen et al [13], it actually turns out that expectile is the only elicitable risk measure within the class of coherent and law invariant risk measures.…”

Section: Introductionmentioning

confidence: 99%

Relative Bound and Asymptotic Comparison of Expectile with Respect to Expected Shortfall

Drapeau¹,

Tadese²

2019

Preprint

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Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to optimized certainty equivalent. Lower and upper bounds of expectile are derived in terms of expected shortfall as well as a characterization of expectile in terms of expected shortfall. Further, we study the asymptotic behavior of expectile with respect to expected shortfall as the risk level goes to 0 in terms of extreme value distributions. Illustrating the formulation of expectile in terms of expected shortfall, we also provide explicit or semi-explicit expressions of expectile for some classical distributions.

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On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles

Cited by 19 publications

References 121 publications

Aggregate Risk Model and Risk Measure-Based Risk Allocation

Aggregate Risk Model and Risk Measure-Based Risk Allocation

Evolución de la medición del riesgo financiero en los últimos 40 años: una panorámica con especial mención en la banca

Relative Bound and Asymptotic Comparison of Expectile with Respect to Expected Shortfall

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