Parameter Uncertainty and Residual Estimation Risk

Bignozzi, Valeria; Tsanakas, Andreas

doi:10.1111/jori.12075

Cited by 36 publications

(27 citation statements)

References 28 publications

(45 reference statements)

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“…Here, we merely define model risk as the risk that the computed portfolio VaR is incorrect as a result of using a misspecified model. Note that a related issue concerns the risk of using model parameters that are estimated, a concern that arises because of the statistical uncertainty of these estimations; we refer to Bignozzi and Tsanakas for a study on the impact of parameter uncertainty on capital adequacy.…”

Section: Var Bounds Of Credit Risk Portfoliosmentioning

confidence: 99%

Value‐at‐Risk Bounds With Variance Constraints

Bernard¹,

Rüschendorf²,

Vanduffel³

2015

J of Risk & Insurance

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We study bounds on the Value-at-Risk (VaR) of a portfolio when besides the marginal distributions of the components its variance is also known, a situation that is of considerable interest in risk management. We discuss when the bounds are sharp (attainable) and also point out a new connection between the study of VaR bounds and the convex ordering of aggregate risk. This connection leads to the construction of an algorithm, called Extended Rearrangement Algorithm (ERA), that makes it possible to approximate sharp VaR bounds. We test the stability and the quality of the algorithm in several numerical examples. We apply the results to the case of credit risk portfolio models and verify that adding the variance constraint gives rise to significantly tighter bounds in all situations of interest. IntroductionIn this article, we study bounds on the Value-at-Risk (VaR) of sums of risks with known marginal distributions (describing the stand-alone risks) under the additional constraint that a bound on the variance of the sum is known. The variance of the sum partially describes the dependence among the risks, as it involves their correlations. This setting is of significant interest as in many practical situations it corresponds closely to the maximum information at hand when assessing the VaR of a portfolio. For example, in the context of credit risk portfolio models, one typically has knowledge regarding the marginal risks (through the so-called PD, EAD, and LGD models), and the variance of the aggregate risk (sum of the individual losses) is also often available, as obtained from default correlation models or through statistical analysis of observed

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Section: Var Bounds Of Credit Risk Portfoliosmentioning

confidence: 99%

Value‐at‐Risk Bounds With Variance Constraints

Bernard¹,

Rüschendorf²,

Vanduffel³

2015

J of Risk & Insurance

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show abstract

“…Fröhlich, A. Weng Similar reservations can be expressed concerning the approach suggested in [2] to increase the risk capital by a capital add-on reflecting the residual risk due to parameter uncertainty. 4 An approach based on a change of perspective 4…”

Section: Adjusting the Risk Capitalmentioning

confidence: 92%

“…[6,7,14,16]), by the Bayesian approach (see e.g. [3,6,7,11,16]), by the raise of confidence level [11] or by a capital add-on (residual risk) [2]. Before proceeding by a discussion of these ideas we summarize results of [11] demonstrating that parameter uncertainty cannot be neglected.…”

Section: Previous Approachesmentioning

confidence: 98%

“…Sect. 3.4 also covers the idea of Bignozzi and Tsanakas [2] of calculating a capital add-on in terms of the residual risk.…”

Section: Introductionmentioning

confidence: 97%

“…This is achieved in [11] by raising the confidence level. In [2] the calculation of a capital add-on in terms of ''residual estimation risk'' is suggested. We discuss these approaches in Sect.…”

Section: Introductionmentioning

confidence: 99%

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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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Assessing model risk in financial and energy markets using dynamic conditional VaRs

Gianfreda,

Scandolo

2023

Appl Stoch Models Bus & Ind

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It has been recognized that model risk has an important effect on any risk measurement procedures, particularly when dealing with complex markets and in the presence of a wide range of implemented models. We consider a normalized measure of model risk for the forecast of daily Value‐at‐Risk, combined with a model selection and an averaging procedure. This allows us to restrict the set of plausible models on a daily basis, making the initial choice of competing models less crucial and then yielding a more reliable assessment of model risk. Using AR‐GARCH‐type models with different distributions for the innovations, we assess the dynamics of model risk for different financial assets (a stock, an equity index, an exchange rate) and commodities (electricity, crude oil and natural gas) over 15 years.

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Parameter Uncertainty and Residual Estimation Risk

Cited by 36 publications

References 28 publications

Value‐at‐Risk Bounds With Variance Constraints

Value‐at‐Risk Bounds With Variance Constraints

Modelling parameter uncertainty for risk capital calculation

Assessing model risk in financial and energy markets using dynamic conditional VaRs

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