Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

Kratz, Marie

doi:10.1007/s10687-014-0197-6

Cited by 16 publications

(15 citation statements)

References 37 publications

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“…Having an explicit formula (8) for the pdf f n of the aggregate risk S n , we can deduce its cdf F Sn integrating f n , and any risk measure based on F Sn , as e.g. the two standard risk measures VaR and TVaR.…”

Section: Analytical Resultsmentioning

confidence: 99%

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Explicit Diversification Benefit for Dependent Risks

Dacorogna¹,

Elbahtouri²,

Kratz

2015

SSRN Journal

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We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence.

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Section: Analytical Resultsmentioning

confidence: 99%

“…when the threshold κ tends to 1), for which Feller's result (see [4]) is available. For sharper and not necessarily asymptotic results, computations could be done using the Normex method (see [8]).…”

Section: Independent Pareto Rv's Case With Asymptotic Threshold (κ 1)mentioning

confidence: 99%

Explicit Diversification Benefit for Dependent Risks

Dacorogna¹,

Elbahtouri²,

Kratz

2015

SSRN Journal

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“…It is a good news since, in practice, typically only the marginal loss distribution functions are known or statistically estimated, while the dependence structure between the losses is either completely or partially unknown." In Kratz [44], a new approach, called Normex, is developed to provide accurate estimates of high quantiles for aggregated independent heavy tailed risks. This method depends only weakly upon the sample size and gives good results for any non-negative tail index of the risks.…”

Section: When Is Value-at-risk Subadditive?mentioning

confidence: 99%

What is the best risk measure in practice? A comparison of standard measures

Emmer¹,

Kratz²,

Tasche³

2015

JOR

211

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Expected shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to value-at-risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable, which means that backtesting for ES is less straightforward than, for example, backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit the commonly accepted desirable properties of risk measures such as coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and expectiles with regard to whether or not they enjoy these properties, with particular emphasis on expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. As a consequence, there is no sufficient evidence to justify an all-inclusive replacement of ES by expectiles in applications. For backtesting ES, we propose an empirical approach that consists of replacing ES by a set of four quantiles, which should allow us to make use of backtesting methods for VaR.

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“…Several hybrid models have been proposed in such context, combining two or more densities (see e.g. [1,7,21,30,32,36,38,39,44,60]).…”

Section: Introductionmentioning

confidence: 99%

“…How many components of the hybrid model to consider and how to choose them? Since we are interested in fitting the whole distribution underlying heavy tailed data, the idea is to consider both the mean and tail behaviors, and to use limit theorems for each one (as suggested and developed analytically in [32]), in order to make the model as general as possible. Therefore, we introduce a Gaussian distribution for the mean behavior, justified by the Central Limit Theorem (CLT), and a GPD for the tail, as the Pickands theorem (see [48]) tells us that the tail of the distribution may be evaluated through a GPD above a high threshold.…”

Section: Introductionmentioning

confidence: 99%

A Self-Calibrating Method for Heavy Tailed Data Modeling: Application in Neuroscience and Finance

2016

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Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why one often resorts to non-parametric approaches. However, when the multiple components are separable, parametric modelling becomes again tractable. In this study, we propose a self-calibrating method to model multi-component data that exhibit heavy tails. We introduce a three-component hybrid distribution: a Gaussian distribution is linked to a Generalized Pareto one via an exponential distribution that bridges the gap between mean and tail behaviors. An unsupervised algorithm is then developed for estimating the parameters of this model. We study analytically and numerically its convergence. The effectiveness of the self-calibrating method is tested on simulated data, before applying it to real data from neuroscience and finance, respectively. A comparison with other standard Extreme Value Theory approaches confirms the relevance and the practical advantage of this new method.

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Normex, a new method for evaluating the distribution of aggregated heavy tailed risks

Cited by 16 publications

References 37 publications

Explicit Diversification Benefit for Dependent Risks

Explicit Diversification Benefit for Dependent Risks

What is the best risk measure in practice? A comparison of standard measures

A Self-Calibrating Method for Heavy Tailed Data Modeling: Application in Neuroscience and Finance

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