Fast remote but not extreme quantiles with multiple factors: applications to Solvency II and Enterprise Risk Management

Chauvigny, Matthieu; Devineau, Laurent; Loisel, Stéphane; Maume-Deschamps, Véronique

doi:10.1007/s13385-011-0034-0

Cited by 5 publications

(4 citation statements)

References 12 publications

(5 reference statements)

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“…Also, rather than space-filling the given Z, it could be desirable to focus further on the respective extreme regions, in the sense of geometrically extremal points of Z, see e.g. the use of statistical depth functions in [11].…”

Section: Discussionmentioning

confidence: 99%

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Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement

Risk¹,

Ludkovski²

2018

SIAM J. Finan. Math.

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We consider calculation of capital requirements when the underlying economic scenarios are determined by simulatable risk factors. In the respective nested simulation framework, the goal is to estimate portfolio tail risk, quantified via VaR or TVaR of a given collection of future economic scenarios representing factor levels at the risk horizon. Traditionally, evaluating portfolio losses of an outer scenario is done by computing a conditional expectation via innerlevel Monte Carlo and is computationally expensive. We introduce several inter-related machine learning techniques to speed up this computation, in particular by properly accounting for the simulation noise. Our main workhorse is an advanced Gaussian Process (GP) regression approach which uses nonparametric spatial modeling to efficiently learn the relationship between the stochastic factors defining scenarios and corresponding portfolio value. Leveraging this emulator, we develop sequential algorithms that adaptively allocate inner simulation budgets to target the quantile region. The GP framework also yields better uncertainty quantification for the resulting VaR / TVaR estimators that reduces bias and variance compared to existing methods. We illustrate the proposed strategies with two case-studies in two and six dimensions.

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Section: Discussionmentioning

confidence: 99%

“…Latin Hypercube sampling, LHS). Chauvigny et al [11] provides a more elaborate method using statistical depth functions to identify pilot scenarios based on the geometry of Z.…”

Section: Initialization Of Fmentioning

confidence: 99%

Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement

Risk¹,

Ludkovski²

2018

SIAM J. Finan. Math.

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“…Proposition 2.4 Consider a random vector X satisfying the regularity conditions. Assume that its multivariate distribution function F is quasi concave 6 . Then, for all α ∈ (0, 1), the following inequalities hold…”

Section: Comparison Of Univariate and Multivariate Varmentioning

confidence: 99%

On multivariate extensions of Value-at-Risk

Cousin

Bernardino

2013

Journal of Multivariate Analysis

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In this paper, we introduce two alternative extensions of the classical univariate Value-at-Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued measures with the same dimension as the underlying risk portfolio. The lower-orthant VaR is constructed from level sets of multivariate distribution functions whereas the upper-orthant VaR is constructed from level sets of multivariate survival functions. Several properties have been derived. In particular, we show that these risk measures both satisfy the positive homogeneity and the translation invariance property. Comparison between univariate risk measures and components of multivariate VaR are provided. We also analyze how these measures are impacted by a change in marginal distributions, by a change in dependence structure and by a change in risk level. Illustrations are given in the class of Archimedean copulas.

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“…Another approach is to use geometric quantiles (see, for example, Chaouch et al (2009)). Along with the geometric quantile, the notion of depth function has been developed in recent years to characterize the quantile of multidimensional distribution functions (for further details see, for instance, Chauvigny et al (2011)). We refer to Serfling (2002) for a review of multivariate quantiles.…”

Section: Introductionmentioning

confidence: 99%

On multivariate extensions of Conditional-Tail-Expectation

Cousin

Bernardino

2014

Insurance: Mathematics and Economics

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In this paper, we introduce two alternative extensions of the classical univariate Conditional-Tail-Expectation (CTE) in a multivariate setting. The two proposed multivariate CTE are vector-valued measures with the same dimension as the underlying risk portfolio. As for the multivariate Valueat-Risk measures introduced in Cousin and Di Bernardino (2013), the lower-orthant CTE (resp. the upper-orthant CTE) is constructed from level sets of multivariate distribution functions (resp. of multivariate survival distribution functions). Contrary to allocation measures or systemic risk measures, these measures are also suitable for multivariate risk problems where risks are heterogenous in nature and cannot be aggregated together. Several properties have been derived. In particular, we show that the proposed multivariate CTE-s satisfy natural extensions of the positive homogeneity property, the translation invariance property and the comonotonic additivity property. Comparison between univariate risk measures and components of multivariate CTE are provided. We also analyze how these measures are impacted by a change in marginal distributions, by a change in dependence structure and by a change in risk level. Sub-additivity of the proposed multivariate CTE-s is provided under the assumption that all components of the random vectors are independent. Illustrations are given in the class of Archimedean copulas.

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Fast remote but not extreme quantiles with multiple factors: applications to Solvency II and Enterprise Risk Management

Cited by 5 publications

References 12 publications

Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement

Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement

On multivariate extensions of Value-at-Risk

On multivariate extensions of Conditional-Tail-Expectation

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