Robust measurement of (heavy-tailed) risks

Theory and implementation

Judith C. Schneider*, Nikolaus Schweizer

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case. Moreover, we present a novel, empirical way built on model confidence sets (MCS) for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. We demonstrate the implications of heavy-tailed risks for the choice of the divergence measure and the empirical divergence estimation. For heavy-tailed risks, the simulation of the worst-case distribution is numerically intricate. We present a Sequential Monte Carlo algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach. (C) 2015 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)183-203
JournalJournal of Economic Dynamics and Control
Volume61
DOIs
Publication statusPublished - Dec 2015
Externally publishedYes

Keywords

  • Divergence estimation
  • Model risk
  • Risk management
  • Robustness
  • Sequential Monte Carlo

Cite this

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title = "Robust measurement of (heavy-tailed) risks: Theory and implementation",
abstract = "Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case. Moreover, we present a novel, empirical way built on model confidence sets (MCS) for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. We demonstrate the implications of heavy-tailed risks for the choice of the divergence measure and the empirical divergence estimation. For heavy-tailed risks, the simulation of the worst-case distribution is numerically intricate. We present a Sequential Monte Carlo algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach. (C) 2015 Elsevier B.V. All rights reserved.",
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Robust measurement of (heavy-tailed) risks : Theory and implementation. / Schneider, Judith C.; Schweizer, Nikolaus.

In: Journal of Economic Dynamics and Control, Vol. 61, 12.2015, p. 183-203.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Robust measurement of (heavy-tailed) risks

T2 - Theory and implementation

AU - Schneider, Judith C.

AU - Schweizer, Nikolaus

PY - 2015/12

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N2 - Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case. Moreover, we present a novel, empirical way built on model confidence sets (MCS) for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. We demonstrate the implications of heavy-tailed risks for the choice of the divergence measure and the empirical divergence estimation. For heavy-tailed risks, the simulation of the worst-case distribution is numerically intricate. We present a Sequential Monte Carlo algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach. (C) 2015 Elsevier B.V. All rights reserved.

AB - Every model presents an approximation of reality and thus modeling inevitably implies model risk. We quantify model risk in a non-parametric way, i.e., in terms of the divergence from a so-called nominal model. Worst-case risk is defined as the maximal risk among all models within a given divergence ball. We derive several new results on how different divergence measures affect the worst case. Moreover, we present a novel, empirical way built on model confidence sets (MCS) for choosing the radius of the divergence ball around the nominal model, i.e., for calibrating the amount of model risk. We demonstrate the implications of heavy-tailed risks for the choice of the divergence measure and the empirical divergence estimation. For heavy-tailed risks, the simulation of the worst-case distribution is numerically intricate. We present a Sequential Monte Carlo algorithm which is suitable for this task. An extended practical example, assessing the robustness of a hedging strategy, illustrates our approach. (C) 2015 Elsevier B.V. All rights reserved.

KW - Divergence estimation

KW - Model risk

KW - Risk management

KW - Robustness

KW - Sequential Monte Carlo

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DO - 10.1016/j.jedc.2015.09.010

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