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The Lila distribution and its applications in risk modelling

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Abstract

Risk date sets tend to have heavy-tailed, sometimes bi-modal, empirical distributions, especially in operational risk, market risk and customers behaviour data sets. To capture these observed “unusual” features, we construct a new probability distribution and call it the lowered-inside-leveraged-aside (Lila) distribution as it transfers the embedded weight of data from the body to the tail. This newly constructed distribution can be viewed as a parametric distribution with two peaks. It is constructed through the composition of a Sigmoid-shaped continuous increasing differentiable function with cumulative distribution functions of random variables. Examples and some basic properties of the Lila distribution are illustrated. As an application, we fit a Lila distribution to a set of generated data by using the quantile distance minimisation method (alternative methodologies have been tested too, such as maximum likelihood estimation)

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  • 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.
    • Handle: RePEc:mse:cesdoc:16068
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    References listed on IDEAS

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    1. Dominique Guégan & Bertrand Hassani, 2015. "Distortion Risk Measure or the Transformation of Unimodal Distributions into Multimodal Functions," International Series in Operations Research & Management Science, in: Alain Bensoussan & Dominique Guegan & Charles S. Tapiero (ed.), Future Perspectives in Risk Models and Finance, edition 127, pages 71-88, Springer.
    2. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    3. Hamada, Mahmoud & Sherris, Michael & Hoek, John van der, 2006. "Dynamic Portfolio Allocation, the Dual Theory of Choice and Probability Distortion Functions," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 187-217, May.
    4. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," PSE-Ecole d'économie de Paris (Postprint) halshs-00443846, HAL.
    5. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    6. 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.
    7. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Post-Print halshs-00443846, HAL.
    8. Xuan Mao, Chang, 2007. "Estimating population sizes for capture-recapture sampling with binomial mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5211-5219, July.
    9. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    Cited by:

    1. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01491990, HAL.
    2. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    3. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Post-Print halshs-01491990, HAL.
    4. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Impact of multimodality of distributions on VaR and ES calculations," Documents de travail du Centre d'Economie de la Sorbonne 17019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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    More about this item

    Keywords

    probability distribution; parametric distribution; multimodal distribution; operational risk; market risk; pseudo bi-modal distribution;
    All these keywords.

    JEL classification:

    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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