IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-00443846.html
   My bibliography  Save this paper

A modified Panjer algorithm for operational risk capital calculations

Author

Listed:
  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Bertrand Hassani

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Operational risk management inside banks and insurance companies is an important task. The computation of a risk measure associated to these kinds of risks lies in the knowledge of the so-called loss distribution function (LDF). Traditionally, this LDF is computed via Monte Carlo simulations or using the Panjer recursion, which is an iterative algorithm. In this paper, we propose an adaptation of this last algorithm in order to improve the computation of convolutions between Panjer class distributions and continuous distributions, by mixing the Monte Carlo method, a progressive kernel lattice and the Panjer recursion. This new hybrid algorithm does not face the traditional drawbacks. This simple approach enables us to drastically reduce the variance of the estimated value-at-risk associated with the operational risks and to lower the aliasing error we would have using Panjer recursion itself. Furthermore, this method is much less timeconsuming than a Monte Carlo simulation. We compare our new method with more sophisticated approaches already developed in operational risk literature.

Suggested Citation

  • Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00443846, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00443846
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00443846v1
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-00443846v1/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
    2. Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bertrand K. Hassani & Wei Yang, 2016. "The Lila distribution and its applications in risk modelling," Documents de travail du Centre d'Economie de la Sorbonne 16068, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Dominique Guegan & Bertrand Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01169268, HAL.
    3. Bertrand K. Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Post-Print halshs-01020293, HAL.
    4. Chih-Kang Chu & Ruey-Ching Hwang, 2019. "Predicting Loss Distributions for Small-Size Defaulted-Debt Portfolios Using a Convolution Technique that Allows Probability Masses to Occur at Boundary Points," Journal of Financial Services Research, Springer;Western Finance Association, vol. 56(1), pages 95-117, August.
    5. Bertrand K Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Documents de travail du Centre d'Economie de la Sorbonne 14037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Dominique Guegan & Bertrand Hassani, 2012. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Post-Print halshs-00587706, HAL.
    7. Vasileios M. Koutras & Markos V. Koutras, 2020. "Exact Distribution of Random Order Statistics and Applications in Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1539-1558, December.
    8. Bertrand K. Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020293, HAL.
    9. Dominique Guegan & Wayne Tarrant, 2012. "On the Necessity of Five Risk Measures," Post-Print halshs-00721339, HAL.
    10. Dominique Guegan & Bertrand Hassani, 2012. "Operational risk : A Basel II++ step before Basel III," PSE-Ecole d'économie de Paris (Postprint) halshs-00722029, HAL.
    11. Dominique Guegan & Bertrand Hassani, 2011. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Documents de travail du Centre d'Economie de la Sorbonne 11017rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Apr 2012.
    12. Dominique Gu�gan & Bertrand Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Working Papers 2015:18, Department of Economics, University of Venice "Ca' Foscari".
    13. Dominique Guegan & Bertrand K Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Documents de travail du Centre d'Economie de la Sorbonne 15046, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    14. Dominique Guegan & Wayne Tarrant, 2012. "On the Necessity of Five Risk Measures," PSE-Ecole d'économie de Paris (Postprint) halshs-00721339, HAL.
    15. Vasileios M. Koutras & Markos V. Koutras & Spiros D. Dafnis, 2022. "A Family of Induced Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1833-1848, September.
    16. Dominique Guegan & Bertrand Hassani, 2012. "Operational risk : A Basel II++ step before Basel III," Post-Print halshs-00722029, HAL.
    17. Dominique Guegan & Bertrand Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Post-Print halshs-01169268, HAL.
    18. Dominique Guegan & Bertrand Hassani, 2014. "Stress Testing Engineering: the real risk measurement?," Post-Print halshs-00951593, HAL.
    19. Bertrand K. Hassani & Wei Yang, 2016. "The Lila distribution and its applications in risk modelling," Post-Print halshs-01400186, HAL.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gareth W. Peters & Pavel V. Shevchenko & Mario V. Wuthrich, 2009. "Dynamic operational risk: modeling dependence and combining different sources of information," Papers 0904.4074, arXiv.org, revised Jul 2009.
    2. Pavel V. Shevchenko, 2009. "Implementing Loss Distribution Approach for Operational Risk," Papers 0904.1805, arXiv.org, revised Jul 2009.
    3. Dominique Guegan & Bertrand Hassani, 2009. "A new algorithm for the loss distribution function with applications to Operational Risk Management," Documents de travail du Centre d'Economie de la Sorbonne 09023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    4. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    5. Winter, Peter, 2007. "Managerial Risk Accounting and Control – A German perspective," MPRA Paper 8185, University Library of Munich, Germany.
    6. Cui, Xueting & Zhu, Shushang & Sun, Xiaoling & Li, Duan, 2013. "Nonlinear portfolio selection using approximate parametric Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(6), pages 2124-2139.
    7. Jay Cao & Jacky Chen & John Hull & Zissis Poulos, 2021. "Deep Hedging of Derivatives Using Reinforcement Learning," Papers 2103.16409, arXiv.org.
    8. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    9. Dimitrios G. Konstantinides & Georgios C. Zachos, 2019. "Exhibiting Abnormal Returns Under a Risk Averse Strategy," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 551-566, June.
    10. Parrini, Alessandro, 2013. "Importance Sampling for Portfolio Credit Risk in Factor Copula Models," MPRA Paper 103745, University Library of Munich, Germany.
    11. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    12. Boonen, Tim J. & Liu, Fangda, 2022. "Insurance with heterogeneous preferences," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    13. Arturo Cortés Aguilar, 2011. "Estimación del residual de un bono respaldado por hipotecas mediante un modelo de riesgo crédito: una comparación de resultados de la teoría de cópulas y el modelo IRB de Basilea II en datos del merca," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 5(1), pages 50-64.
    14. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    15. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    16. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    17. Kull, Andreas, 2009. "Sharing Risk – An Economic Perspective," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 591-613, November.
    18. Schumacher Johannes M., 2018. "Distortion risk measures, ROC curves, and distortion divergence," Statistics & Risk Modeling, De Gruyter, vol. 35(1-2), pages 35-50, January.
    19. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    20. Oliver Linton & Dajing Shang & Yang Yan, 2012. "Efficient estimation of conditional risk measures in a semiparametric GARCH model," CeMMAP working papers CWP25/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00443846. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.