Multi-Variate Risk Measures under Wasserstein Barycenter
When the uni-variate risk measure analysis is generalized into the multi-variate setting, many complex theoretical and applied problems arise, and therefore the mathematical models used for risk quantification usually present model risk. As a result, regulators have started to require that the inter...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Risks |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-9091/10/9/180 |
| _version_ | 1797482721859076096 |
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| author | M. Andrea Arias-Serna Jean Michel Loubes Francisco J. Caro-Lopera |
| author_facet | M. Andrea Arias-Serna Jean Michel Loubes Francisco J. Caro-Lopera |
| author_sort | M. Andrea Arias-Serna |
| collection | DOAJ |
| description | When the uni-variate risk measure analysis is generalized into the multi-variate setting, many complex theoretical and applied problems arise, and therefore the mathematical models used for risk quantification usually present model risk. As a result, regulators have started to require that the internal models used by financial institutions are more precise. For this task, we propose a novel multi-variate risk measure, based on the notion of the Wasserstein barycenter. The proposed approach robustly characterizes the company’s exposure, filtering the partial information available from individual sources into an aggregate risk measure, providing an easily computable estimation of the total risk incurred. The new approach allows effective computation of Wasserstein barycenter risk measures in any location–scatter family, including the Gaussian case. In such cases, the Wasserstein barycenter Value-at-Risk belongs to the same family, thus it is characterized just by its mean and deviation. It is important to highlight that the proposed risk measure is expressed in closed analytic forms which facilitate its use in day-to-day risk management. The performance of the new multi-variate risk measures is illustrated in United States market indices of high volatility during the global financial crisis (2008) and during the COVID-19 pandemic situation, showing that the proposed approach provides the best forecasts of risk measures not only for “normal periods”, but also for periods of high volatility. |
| first_indexed | 2024-03-09T22:36:32Z |
| format | Article |
| id | doaj.art-316e5fdb54884fd58f35652090d6074d |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-09T22:36:32Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-316e5fdb54884fd58f35652090d6074d2023-11-23T18:47:21ZengMDPI AGRisks2227-90912022-09-0110918010.3390/risks10090180Multi-Variate Risk Measures under Wasserstein BarycenterM. Andrea Arias-Serna0Jean Michel Loubes1Francisco J. Caro-Lopera2Faculty of Engineering, University of Medellin, Medellin 050026, ColombiaInstitut de Mathématiques de Toulouse, University of Toulouse, 31062 Toulouse, FranceFaculty of Basic Sciences, University of Medellin, Medellin 050026, ColombiaWhen the uni-variate risk measure analysis is generalized into the multi-variate setting, many complex theoretical and applied problems arise, and therefore the mathematical models used for risk quantification usually present model risk. As a result, regulators have started to require that the internal models used by financial institutions are more precise. For this task, we propose a novel multi-variate risk measure, based on the notion of the Wasserstein barycenter. The proposed approach robustly characterizes the company’s exposure, filtering the partial information available from individual sources into an aggregate risk measure, providing an easily computable estimation of the total risk incurred. The new approach allows effective computation of Wasserstein barycenter risk measures in any location–scatter family, including the Gaussian case. In such cases, the Wasserstein barycenter Value-at-Risk belongs to the same family, thus it is characterized just by its mean and deviation. It is important to highlight that the proposed risk measure is expressed in closed analytic forms which facilitate its use in day-to-day risk management. The performance of the new multi-variate risk measures is illustrated in United States market indices of high volatility during the global financial crisis (2008) and during the COVID-19 pandemic situation, showing that the proposed approach provides the best forecasts of risk measures not only for “normal periods”, but also for periods of high volatility.https://www.mdpi.com/2227-9091/10/9/180wasserstein barycentermulti-variate risk measuresvalue-at-riskconditional value-at-risklocation–scatter distributions |
| spellingShingle | M. Andrea Arias-Serna Jean Michel Loubes Francisco J. Caro-Lopera Multi-Variate Risk Measures under Wasserstein Barycenter Risks wasserstein barycenter multi-variate risk measures value-at-risk conditional value-at-risk location–scatter distributions |
| title | Multi-Variate Risk Measures under Wasserstein Barycenter |
| title_full | Multi-Variate Risk Measures under Wasserstein Barycenter |
| title_fullStr | Multi-Variate Risk Measures under Wasserstein Barycenter |
| title_full_unstemmed | Multi-Variate Risk Measures under Wasserstein Barycenter |
| title_short | Multi-Variate Risk Measures under Wasserstein Barycenter |
| title_sort | multi variate risk measures under wasserstein barycenter |
| topic | wasserstein barycenter multi-variate risk measures value-at-risk conditional value-at-risk location–scatter distributions |
| url | https://www.mdpi.com/2227-9091/10/9/180 |
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