IDEAS home Printed from https://ideas.repec.org/p/hal/journl/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 des Ponts ParisTech - 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," Post-Print halshs-00443846, HAL.
    • Handle: RePEc:hal:journl:halshs-00443846
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00443846
    as

    Download full text from publisher

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

    References listed on IDEAS

    as
    1. 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.
    2. Grübel, Rudolf & Hermesmeier, Renate, 1999. "Computation of Compound Distributions I: Aliasing Errors and Exponential Tilting," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 197-214, November.
    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, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01020293, HAL.
    2. Dominique Guégan & Wayne Tarrant, 2012. "On the necessity of five risk measures," Annals of Finance, Springer, vol. 8(4), pages 533-552, November.
    3. 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.
    4. Dominique Guegan & Wayne Tarrant, 2012. "On the Necessity of Five Risk Measures," Post-Print halshs-00721339, HAL.
    5. Dominique Guegan & Bertrand Hassani, 2012. "Operational risk : A Basel II++ step before Basel III," PSE-Ecole d'économie de Paris (Postprint) halshs-00722029, HAL.
    6. 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.
    7. 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.
    8. Bertrand K. Hassani, 2014. "Risk Appetite in Practice: Vulgaris Mathematica," Post-Print halshs-01020293, HAL.
    9. 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".
    10. 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.
    11. 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.
    12. Dominique Guegan & Wayne Tarrant, 2012. "On the Necessity of Five Risk Measures," PSE-Ecole d'économie de Paris (Postprint) halshs-00721339, HAL.
    13. 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.
    14. 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.
    15. Dominique Guegan & Bertrand Hassani, 2012. "Multivariate VaRs for Operational Risk Capital Computation: a Vine Structure Approach," Post-Print halshs-00587706, HAL.
    16. Dominique Guegan & Bertrand Hassani, 2012. "Operational risk : A Basel II++ step before Basel III," Post-Print halshs-00722029, HAL.
    17. 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.
    18. Dominique Guegan & Bertrand Hassani, 2015. "Risk or Regulatory Capital? Bringing distributions back in the foreground," Post-Print halshs-01169268, HAL.
    19. Dominique Guegan & Bertrand Hassani, 2014. "Stress Testing Engineering: the real risk measurement?," Post-Print halshs-00951593, HAL.
    20. 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. Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
    2. 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.
    3. Dominique Guegan & Bertrand Hassani, 2009. "A new algorithm for the loss distribution function with applications to Operational Risk Management," Post-Print halshs-00384398, HAL.
    4. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
    5. 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.
    6. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    7. Nicola Bruti-Liberati & Eckhard Platen, 2007. "Approximation of jump diffusions in finance and economics," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 283-312, May.
    8. Xiaolin Luo & Pavel V. Shevchenko & John B. Donnelly, 2009. "Addressing the Impact of Data Truncation and Parameter Uncertainty on Operational Risk Estimates," Papers 0904.2910, arXiv.org.
    9. Paul Embrechts & Marco Frei, 2009. "Panjer recursion versus FFT for compound distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 497-508, July.
    10. Valeriy A. Naumov & Yuliya V. Gaidamaka & Konstantin E. Samouylov, 2020. "Computing the Stationary Distribution of Queueing Systems with Random Resource Requirements via Fast Fourier Transform," Mathematics, MDPI, vol. 8(5), pages 1-9, May.
    11. Cruz Báez, Domingo Israel & González Rodríguez, José Manuel, 2008. "Valoración de opciones. Un enfoque diferente," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 26, pages 341-362, Abril.
    12. C. Atkinson & S. Kazantzaki, 2009. "Double knock-out Asian barrier options which widen or contract as they approach maturity," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 329-340.
    13. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    14. Li Qin & Susan M. Pitts, 2012. "Nonparametric Estimation of the Finite-Time Survival Probability with Zero Initial Capital in the Classical Risk Model," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 919-936, December.
    15. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19, July-Dece.
    16. Kwai Sun Leung & Yue Kuen Kwok, 2008. "Employee stock option valuation with repricing features," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 561-569.
    17. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2009, January-A.
    18. Mark Craddock & Eckhard Platen, 2003. "Symmetry Group Methods for Fundamental Solutions and Characteristic Functions," Research Paper Series 90, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    20. Richard L. Warr & Cason J. Wight, 2020. "Error Bounds for Cumulative Distribution Functions of Convolutions via the Discrete Fourier Transform," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 881-904, September.

    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:journl: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.