IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v7y2019i2p50-d227534.html
   My bibliography  Save this article

Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement

Author

Listed:
  • Francesca Greselin

    (Department of Statistics and Quantitative Methods, Milano-Bicocca University, 20126 Milano, Italy
    These authors contributed equally to this work.)

  • Fabio Piacenza

    (Group Operational and Reputational Risks, UniCredit S.p.A., 20154 Milano, Italy
    These authors contributed equally to this work.)

  • Ričardas Zitikis

    (School of Mathematical and Statistical Sciences, Western University, London, ON N6A 5B7, Canada
    These authors contributed equally to this work.
    Research of the third author has been supported by the Natural Sciences and Engineering Research Council of Canada under the title “From Data to Integrated Risk Management and Smart Living: Mathematical Modelling, Statistical Inference, and Decision Making,” as well as by a Mitacs Accelerate Award from the national research organization Mathematics of Information Technology and Complex Systems, Canada, in partnership with Sun Life Financial, under the title “Risk Aggregation Beyond the Normal Limits.”)

Abstract

We explore the Monte Carlo steps required to reduce the sampling error of the estimated 99.9% quantile within an acceptable threshold. Our research is of primary interest to practitioners working in the area of operational risk measurement, where the annual loss distribution cannot be analytically determined in advance. Usually, the frequency and the severity distributions should be adequately combined and elaborated with Monte Carlo methods, in order to estimate the loss distributions and risk measures. Naturally, financial analysts and regulators are interested in mitigating sampling errors, as prescribed in EU Regulation 2018/959. In particular, the sampling error of the 99.9% quantile is of paramount importance, along the lines of EU Regulation 575/2013. The Monte Carlo error for the operational risk measure is here assessed on the basis of the binomial distribution. Our approach is then applied to realistic simulated data, yielding a comparable precision of the estimate with a much lower computational effort, when compared to bootstrap, Monte Carlo repetition, and two other methods based on numerical optimization.

Suggested Citation

  • Francesca Greselin & Fabio Piacenza & Ričardas Zitikis, 2019. "Practice Oriented and Monte Carlo Based Estimation of the Value-at-Risk for Operational Risk Measurement," Risks, MDPI, vol. 7(2), pages 1-20, May.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:2:p:50-:d:227534
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/7/2/50/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/7/2/50/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dalla Valle, L. & Giudici, P., 2008. "A Bayesian approach to estimate the marginal loss distributions in operational risk management," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3107-3127, February.
    2. Casper De Vries & Jon Danielsson & Casper G, de Vries, 1996. "Tail Index and Quantile Estimation with Very High Frequency Data," CESifo Working Paper Series 116, CESifo.
    3. 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.
    4. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2017. "Measuring firm size distribution with semi-nonparametric densities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 35-47.
    5. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    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. Teodora Maria SUCIU (AVRAM), 2020. "Possibilities Of Evaluation Of The Expenditure Of The Clothing Industry By The Monte Carlo Method," Contemporary Economy Journal, Constantin Brancoveanu University, vol. 5(3), pages 29-37.
    2. Jiandong Ren & Kristina Sendova & Ričardas Zitikis, 2019. "Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”," Risks, MDPI, vol. 7(3), pages 1-7, September.

    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. Iñaki Aldasoro & Leonardo Gambacorta & Paolo Giudici & Thomas Leach, 2023. "Operational and Cyber Risks in the Financial Sector," International Journal of Central Banking, International Journal of Central Banking, vol. 19(5), pages 340-402, December.
    2. Josh Lerner, 2002. "Where Does State Street Lead? A First Look at Finance Patents, 1971 to 2000," Journal of Finance, American Finance Association, vol. 57(2), pages 901-930, April.
    3. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    4. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    5. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    6. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    7. E. Nasakkala & J. Keppo, 2008. "Hydropower with Financial Information," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 503-529.
    8. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    9. Galai, Dan & Raviv, Alon & Wiener, Zvi, 2007. "Liquidation triggers and the valuation of equity and debt," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3604-3620, December.
    10. Joseph Y. J. Chow & Amelia C. Regan, 2011. "Real Option Pricing of Network Design Investments," Transportation Science, INFORMS, vol. 45(1), pages 50-63, February.
    11. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    12. Siem Jan Koopman & Neil Shephard, 2002. "Testing the Assumptions Behind the Use of Importance Sampling," Economics Papers 2002-W17, Economics Group, Nuffield College, University of Oxford.
    13. Sina Atari & Yassine Bakkar & Eunice Omolola Olaniyi & Gunnar Prause, 2019. "Real options analysis of abatement investments for sulphur emission control compliance," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 6(3), pages 1062-1087, March.
    14. Boris Ter-Avanesov & Homayoon Beigi, 2024. "MLP, XGBoost, KAN, TDNN, and LSTM-GRU Hybrid RNN with Attention for SPX and NDX European Call Option Pricing," Papers 2409.06724, arXiv.org, revised Oct 2024.
    15. Kostrova, Alisa & Britz, Wolfgang & Djanibekov, Utkur & Finger, Robert, 2016. "Monte-Carlo Simulation and Stochastic Programming in Real Options Valuation: the Case of Perennial Energy Crop Cultivation," Discussion Papers 250253, University of Bonn, Institute for Food and Resource Economics.
    16. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    17. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    18. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    19. Gonzalo Cortazar & Alejandro Bernales & Diether Beuermann, 2005. "Methodology and Implementation of Value-at-Risk Measures in Emerging Fixed-Income Markets with Infrequent Trading," Finance 0512030, University Library of Munich, Germany.
    20. 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.

    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:gam:jrisks:v:7:y:2019:i:2:p:50-:d:227534. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.