Conditional excess risk measures and multivariate regular variation

2019 ◽  
Vol 36 (1-4) ◽  
pp. 1-23
Author(s):  
Bikramjit Das ◽  
Vicky Fasen-Hartmann
Keyword(s):  
Risk Factors ◽  
Asymptotic Behavior ◽  
Systemic Risk ◽  
Regular Variation ◽  
Risk Measures ◽  
Excess Risk ◽  
Multivariate Regular Variation ◽  
Marginal Expected Shortfall ◽  
Broad Framework ◽  
Heavy Tailed

Abstract Conditional excess risk measures like Marginal Expected Shortfall and Marginal Mean Excess are designed to aid in quantifying systemic risk or risk contagion in a multivariate setting. In the context of insurance, social networks, and telecommunication, risk factors often tend to be heavy-tailed and thus frequently studied under the paradigm of regular variation. We show that regular variation on different subspaces of the Euclidean space leads to these risk measures exhibiting distinct asymptotic behavior. Furthermore, we elicit connections between regular variation on these subspaces and the behavior of tail copula parameters extending previous work and providing a broad framework for studying such risk measures under multivariate regular variation. We use a variety of examples to exhibit where such computations are practically applicable.

Extremes for multivariate expectiles

2018 ◽  
Vol 35 (3-4) ◽  
pp. 111-140
Author(s):  
Véronique Maume-Deschamps ◽  
Didier Rullière ◽  
Khalil Said
Keyword(s):  
Asymptotic Behavior ◽  
Regular Variation ◽  
Risk Measures ◽  
Domain Of Attraction ◽  
Asymptotic Independence ◽  
Multivariate Regular Variation ◽  
Marginal Distributions ◽  
New Family ◽  
Vector Valued

Abstract Multivariate expectiles, a new family of vector-valued risk measures, were recently introduced in the literature. [22]. Here we investigate the asymptotic behavior of these measures in a multivariate regular variation context. For models with equivalent tails, we propose an estimator of extreme multivariate expectiles in the Fréchet domain of attraction case with asymptotic independence, or for comonotonic marginal distributions.

scholarly journals Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions

2009 ◽  
Vol 46 (4) ◽  
pp. 925-937 ◽  
Author(s):  
Haijun Li ◽  
Yannan Sun
Keyword(s):  
Regular Variation ◽  
Tail Dependence ◽  
Heavy Tail ◽  
Sufficient Condition ◽  
Elliptical Distributions ◽  
Multivariate Regular Variation ◽  
Multivariate Distributions ◽  
Scale Mixtures ◽  
Heavy Tailed ◽  
General Method

The tail dependence of multivariate distributions is frequently studied via the tool of copulas. In this paper we develop a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulae for tail dependence parameters are derived, and a sufficient condition under which the parameters are monotone with respect to the heavy tail index is obtained. The multivariate elliptical distributions are discussed to illustrate the results.

scholarly journals Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions

2009 ◽  
Vol 46 (04) ◽  
pp. 925-937 ◽  
Author(s):  
Haijun Li ◽  
Yannan Sun
Keyword(s):  
Regular Variation ◽  
Tail Dependence ◽  
Heavy Tail ◽  
Sufficient Condition ◽  
Elliptical Distributions ◽  
Multivariate Regular Variation ◽  
Multivariate Distributions ◽  
Scale Mixtures ◽  
Heavy Tailed ◽  
General Method

The tail dependence of multivariate distributions is frequently studied via the tool of copulas. In this paper we develop a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulae for tail dependence parameters are derived, and a sufficient condition under which the parameters are monotone with respect to the heavy tail index is obtained. The multivariate elliptical distributions are discussed to illustrate the results.

scholarly journals Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures

2020 ◽  
Author(s):  
Denisa Banulescu-Radu ◽  
Christophe Hurlin ◽  
Jérémy Leymarie ◽  
Olivier Scaillet
Keyword(s):  
At Risk ◽  
Financial Institutions ◽  
Systemic Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Finite Sample ◽  
Marginal Expected Shortfall

This paper proposes an original approach for backtesting systemic risk measures. This backtesting approach makes it possible to assess the systemic risk measure forecasts used to identify the financial institutions that contribute the most to the overall risk in the financial system. Our procedure is based on simple tests similar to those generally used to backtest the standard market risk measures such as value-at-risk or expected shortfall. We introduce a concept of violation associated with the marginal expected shortfall (MES), and we define unconditional coverage and independence tests for these violations. We can generalize these tests to any MES-based systemic risk measures such as the systemic expected shortfall (SES), the systemic risk measure (SRISK), or the delta conditional value-at-risk ([Formula: see text]CoVaR). We study their asymptotic properties in the presence of estimation risk and investigate their finite sample performance via Monte Carlo simulations. An empirical application to a panel of U.S. financial institutions is conducted to assess the validity of MES, SRISK, and [Formula: see text]CoVaR forecasts issued from a bivariate GARCH model with a dynamic conditional correlation structure. Our results show that this model provides valid forecasts for MES and SRISK when considering a medium-term horizon. Finally, we propose an early warning system indicator for future systemic crises deduced from these backtests. Our indicator quantifies how much is the measurement error issued by a systemic risk forecast at a given point in time which can serve for the early detection of global market reversals. This paper was accepted by Kay Giesecke, finance.

ASYMPTOTICS FOR SYSTEMIC RISK WITH DEPENDENT HEAVY-TAILED LOSSES

2021 ◽  
pp. 1-35
Author(s):  
Jiajun Liu ◽  
Yang Yang
Keyword(s):  
Asymptotic Behavior ◽  
Significant Role ◽  
Systemic Risk ◽  
Risk Model ◽  
Dependence Structure ◽  
Entire System ◽  
Simulation Experiments ◽  
Heavy Tailed ◽  
Ideal Framework

Abstract Systemic risk (SR) is considered as the risk of collapse of an entire system, which has played a significant role in explaining the recent financial turmoils from the insurance and financial industries. We consider the asymptotic behavior of the SR for portfolio losses in the model allowing for heavy-tailed primary losses, which are equipped with a wide type of dependence structure. This risk model provides an ideal framework for addressing both heavy-tailedness and dependence. As some extensions, several simulation experiments are conducted, where an insurance application of the asymptotic characterization to the determination and approximation of related SR capital has been proposed, based on the SR measure.

Pitfalls in the Use of Systemic Risk Measures

2018 ◽  
Vol 53 (1) ◽  
pp. 269-298 ◽  
Author(s):  
Gunter Löffler ◽  
Peter Raupach
Keyword(s):  
Side Effects ◽  
Systemic Risk ◽  
Risk Measures ◽  
Systematic Risk ◽  
Idiosyncratic Risk ◽  
Adverse Side Effects ◽  
Heavy Tailed Distributions ◽  
Linear And Nonlinear ◽  
Heavy Tailed

We examine pitfalls in the use of return-based measures of systemic risk contributions (SRCs). For both linear and nonlinear return frameworks, assuming normal and heavy-tailed distributions, we identify nonexotic cases in which a change in a bank’s systematic risk, idiosyncratic risk, size, or contagiousness increases the risk of the system but lowers the measured SRC of the bank. Assessments based on estimated SRCs could thus produce false interpretations and incentives. We also identify potentially adverse side effects: A change in a bank’s risk structure can make the measured SRC of its competitors increase more strongly than its own.

scholarly journals Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures

2019 ◽  
Author(s):  
Denisa Banulescu ◽  
Christophe Hurlin ◽  
Jeremy Leymarie ◽  
Olivier Scaillet
Keyword(s):  
Systemic Risk ◽  
Risk Measures ◽  
Expected Shortfall ◽  
Marginal Expected Shortfall

scholarly journals A Bayesian Entropy Approach to Sectoral Systemic Risk Modeling

Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1371
Author(s):  
Radu Lupu ◽  
Adrian Cantemir Călin ◽  
Cristina Georgiana Zeldea ◽  
Iulia Lupu
Keyword(s):  
Real Estate ◽  
Systemic Risk ◽  
Risk Measures ◽  
Estimation Method ◽  
Spillover Effects ◽  
Expected Shortfall ◽  
Risk Modeling ◽  
Capital Goods ◽  
Entropy Estimation ◽  
Marginal Expected Shortfall

We investigate the dynamics of systemic risk of European companies using an approach that merges paradigmatic risk measures such as Marginal Expected Shortfall, CoVaR, and Delta CoVaR, with a Bayesian entropy estimation method. Our purpose is to bring to light potential spillover effects of the entropy indicator for the systemic risk measures computed on the 24 sectors that compose the STOXX 600 index. Our results show that several sectors have a high proclivity for generating spillovers. In general, the largest influences are delivered by Capital Goods, Banks, Diversified Financials, Insurance, and Real Estate. We also bring detailed evidence on the sectors that are the most pregnable to spillovers and on those that represent the main contributors of spillovers.

A Riskmas Carol

2020 ◽  
pp. 097215092097073
Author(s):  
Matteo Foglia ◽  
Eliana Angelini
Keyword(s):  
Stock Market ◽  
Event Study ◽  
Systemic Risk ◽  
Risk Measures ◽  
Expected Shortfall ◽  
Study Approach ◽  
Santa Claus ◽  
Marginal Expected Shortfall ◽  
Positive Effect ◽  
Systemically Important Banks

Do you believe in Santa Claus (rally)? This study investigates the existence of the ‘Santa Claus rally’ in bank systemic risk. Christmas rally describes a persistent rise in the stock market during the final week of December through the first two trading days in January. In this article, we evaluate this calendar effect, focusing on systemic risk measures for global systemically important banks (GSIBs). First, we estimate the three popular systemic risk measures (DCoVaR, marginal expected shortfall [MES] and SRISK), and then we use an event study approach to analyse the reaction of risk. The results support the existence of Santa Claus. We find that the arrival of Santa Claus has a positive effect on systemic risk, that is, a reduction in bank systemic risk.

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