On multivariate extensions of Value-at-Risk

Cousin, Areski; Bernardino, Éléna Di

doi:10.1016/j.jmva.2013.03.016

Cited by 54 publications

(65 citation statements)

References 27 publications

(39 reference statements)

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“…In particular, Cousin and Di Bernardino [8] proved that properties of the multivariate ConditionalTail-Expectation in (1.1) turn to be consistent with existing properties on univariate risk measures (positive homogeneity, translation invariance, increasing in risk-level c, . .…”

Section: Introductionmentioning

confidence: 57%

“…As a starting point, in the following, we consider the multivariate version of the CTE measure, proposed by Di Bernardino et al [15] and Cousin and Di Bernardino [8]. It is constructed as the conditional expectation of a multivariate random vector given that the latter is located in the c-upper level set of the associated multivariate distribution function.…”

Section: Introductionmentioning

confidence: 99%

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Estimating covariate functions associated to multivariate risks: a level set approach

Bernardino

Laloë

Servien

2014

Metrika

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The aim of this paper is to study the behavior of a covariate function in a multivariate risks scenario. The first part of this paper deals with the problem of estimating the c-upper level sets L(c) = {F (x) ≥ c}, with c ∈ (0, 1), of an unknown distribution function F on R d + . A plug-in approach is followed. We state consistency results with respect to the volume of the symmetric difference. In the second part, we obtain the Lp-consistency, with a convergence rate, for the regression function estimate on these level sets L(c).We also consider a new multivariate risk measure: the Covariate-Conditional-Tail-Expectation. We provide a consistent estimator for this measure with a convergence rate. We propose a consistent estimate when the regression cannot be estimated on the whole data set. Then, we investigate the effects of scaling data on our consistency results. All these results are proven in a non-compact setting. A complete simulation study is detailed. Finally, a real environmental application of our risk measure is provided.

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Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Estimating covariate functions associated to multivariate risks: a level set approach

Bernardino

Laloë

Servien

2014

Metrika

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“…It is also used when some properties are desirable (symmetry, convex level curves, zero-set, associativity, etc.). These properties are used for example in [3,8]. Furthermore, the lower and upper tail dependence behaviours of the copula are directly linked with the regular variation indexes of the generator (see e.g.…”

Section: Discussionmentioning

confidence: 99%

A note on upper-patched generators for Archimedean copulas

Bernardino

Rullière

2017

ESAIM: PS

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Abstract. The class of multivariate Archimedean copulas is defined by using a real-valued function called the generator of the copula. This generator satisfies some properties, including d-monotonicity. We propose here a new basic transformation of this generator, preserving these properties, thus ensuring the validity of the transformed generator and inducing a proper valid copula. This transformation acts only on a specific portion of the generator, it allows both the non-reduction of the likelihood on a given dataset, and the choice of the upper tail dependence coefficient of the transformed copula. Numerical illustrations show the utility of this construction, which can improve the fit of a given copula both on its central part and its tail.Mathematics Subject Classification. 62H20, 62E20, 60E05, 62H05.

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“…In addition, Lee (2011a, 2011b) used copula functions to estimate the VaR of the bivariate and multivariate return rate data. Cousin and Bernardino (2013) extended the definitions of Embrechts and Puccetti (2006) and suggested a multivariate lower-orthant VaR and upper-orthant VaR by using the cumulative distribution function and constructed a survival function of each variable simultaneously. Then, they explored the function properties and relation equations.…”

Section: Introductionmentioning

confidence: 99%

Multivariate CTE for copula distributions

Hong¹,

Kim²

2017

Journal of the Korean Data and Information Science Society

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The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

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On multivariate extensions of Value-at-Risk

Cited by 54 publications

References 27 publications

Estimating covariate functions associated to multivariate risks: a level set approach

Estimating covariate functions associated to multivariate risks: a level set approach

A note on upper-patched generators for Archimedean copulas

Multivariate CTE for copula distributions

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