Risk models-at-risk

Boucher, Christophe; Danı́elsson, Jón; Kouontchou, Patrick; Maillet, Bertrand

doi:10.1016/j.jbankfin.2014.03.019

Cited by 96 publications

(75 citation statements)

References 69 publications

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“…As the DGP is usually unknown, two important sources of model risk are (1) the choice of an inaccurate model, i.e., misspecification risk, and (2) the deviation between the estimated and the true parameter, i.e., estimation risk (see Boucher et al, 2014). In a real-world scenario both sources of risk can not be identified on an isolated basis as they relate to each other and thus, are jointly analyzed.…”

Section: Determination Of Model Riskmentioning

confidence: 99%

“…Moreover, several analyses quantify estimation risk through determining confidence intervals for Value-at-Risk estimates under various model assumptions, i.e., the unconditional normal distribution, historical estimates, conditional GARCH models with different innovation assumptions such as normal or Student t errors, the Hill estimator, filtered historical simulation, Gram-Charlier and Cornish-Fisher expansion (see Pritisker, 1997;Christoffersen and Goncalves, 2005;Chan et al, 2007). Besides this type of model risk quantification, Gourieroux and Zakoyan (2013) and Boucher et al (2014) examine model risk through adjustment factors which need to be added to the original risk measure estimate in order to derive the desired behavior.…”

Section: Introductionmentioning

confidence: 99%

“…We analyze the potential impact of model risk using a simulation and an empirical analysis. Our work builds on Kerkhof et al (2010) and Boucher et al (2014) as we quantify the amount of misspecification and estimation risk (first order effects of model risk) through the determination of adjustment factors by means of numerical optimization. To the best of our knowledge, we are the first to use conditional EVT methods in this context and additionally examine model risk for the expected shortfall under the application of the peaks over threshold method.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The role of model risk in extreme value theory for capital adequacy

Scheule¹,

Kellner²,

Rösch³

2016

JOR

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In the recent literature, methods from extreme value theory (EVT) have frequently been applied for the estimation of tail risk measures. While previous analyses show that EVT methods often lead to accurate estimates for risk measures, a potential drawback lies in high standard errors of point estimates of these methods as only a fraction of the data set is used. Thus, the aim of this paper is to comprehensively study the impact of model risk on EVT methods when determining the Value-at-Risk and Expected Shortfall. We distinguish between first order effects of model risk, which consist of misspecification and estimation risk, and second order effects of model risk which refer to the dispersion of risk measure estimates. We show that EVT methods are less prone to first order effects of model risk, however, they exhibit a higher sensitivity towards second order effects of model risk. We find that this can lead to severe Value-at-Risk and Expected Shortfall underestimations and should be reflected in regulatory capital models.

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Section: Determination Of Model Riskmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The role of model risk in extreme value theory for capital adequacy

Scheule¹,

Kellner²,

Rösch³

2016

JOR

View full text Add to dashboard Cite

show abstract

“…Model uncertainty arising from ignorance of the dependence structure between portfolio risks has been investigated by Embrechts et al (2013). Recently, Boucher et al (2014) proposed an approach to empirically adjust risk measure estimates in order to limit the impact of model uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Model uncertainty in risk capital measurement

Bignozzi¹,

Tsanakas²

2016

JOR

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The required solvency capital for a financial portfolio is typically given by a tail risk measure such as Value-at-Risk. Estimating the value of that risk measure from a limited, often small, sample of data gives rise to potential errors in the selection of the statistical model and the estimation of its parameters. We propose to quantify the effectiveness of a capital estimation procedure via the notions of residual estimation risk and estimated capital risk. It is shown that for capital estimation procedures that do not require the specification of a model (eg historical simulation) or for worst-case scenario procedures the impact of model uncertainty is substantial, while capital estimation procedures that allow for multiple candidate models using Bayesian methods, partially eliminate model error. In the same setting, we propose a way of quantifying model error that allows to disentangle the impact of model uncertainty from that of parameter uncertainty. We illustrate these ideas by simulation examples considering standard loss and return distributions used in banking and insurance.

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“…Note that the idea to consider the SCR as a random variable and to require that this random variable covers the losses with a probability of 99.5 % is not new and goes back to the theory of predictive inference ( [1], [5], [19], Chapter 10, [4,15]). Gerrard and Tsanakas [11] have applied this approach to parameter uncertainty for VaR-based solvency capital calculations.…”

Section: Introductionmentioning

confidence: 99%

Modelling parameter uncertainty for risk capital calculation

Fröhlich¹,

Weng

2015

Eur. Actuar. J.

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For risk capital calculation within the framework of Solvency II the possible loss of basic own funds over the next business year of an insurance undertaking is usually interpreted as a random variable X. If we assume that the parametric distribution family XðhÞjh 2 I R d È É is known, but the parameter h is unknown and has to be estimated from the available historical data, the undertaking faces parameter uncertainty. To assess methods to model parameter uncertainty for risk capital calculations we apply a criterion going back to the theory of predictive inference which has already been used in the context of Solvency II. In particular, we show that the bootstrapping approach is not appropriate to model parameter uncertainty from the undertaking's perspective. Based on ideas closely related to the concept of fiducial inference we introduce a new approach to model parameter uncertainty. For a wide class of distributions and for common estimators including the maximum likelihood method we prove that this approach is appropriate to model parameter uncertainty according to the criterion mentioned above. Several examples demonstrate that our method can easily be applied in practice.

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Risk models-at-risk

Cited by 96 publications

References 69 publications

The role of model risk in extreme value theory for capital adequacy

The role of model risk in extreme value theory for capital adequacy

Model uncertainty in risk capital measurement

Modelling parameter uncertainty for risk capital calculation

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