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Aggregation of Dependent Risks with Specific Marginals by the Family of Koehler-Symanowski Distributions

Author

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  • Paola Palmitesta
  • Corrado Provasi

Abstract

Many problems in Finance, such as risk management, optimal asset allocation, and derivative pricing, require an understanding of the volatility and correlations of assets returns. In these cases, it may be necessary to represent empirical data with a parametric distribution. In the literature, many distributions can be found to represent univariate data, but few can be extended to multivariate populations. The most widely used multivariate distribution in the aggregation of dependent risks in a portfolio is the Normal distribution, which has the drawbacks of inflexibility and frequent inappropriateness. Here, we consider modelling assets and measuring portfolio risks using the family of Koehler-Symanowski multivariate distributions with specific marginals, as, for example, the generalized lambda distribution. This family of distributions can be defined using the cdf along with interaction terms in the independence case. This family can be derived using a particular transformation of exponential random variables and an independent gamma. This distribution has the advantage of allowing models with complex dependence structures, as we demonstrate with Monte Carlo simulations and the analysis of the risk of a portfolio

Suggested Citation

  • Paola Palmitesta & Corrado Provasi, 2004. "Aggregation of Dependent Risks with Specific Marginals by the Family of Koehler-Symanowski Distributions," Computing in Economics and Finance 2004 306, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:306
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    References listed on IDEAS

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    1. Koehler, K. J. & Symanowski, J. T., 1995. "Constructing Multivariate Distributions with Specific Marginal Distributions," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 261-282, November.
    2. Fernández, C. & Steel, M.F.J., 1996. "On Bayesian Modelling of Fat Tails and Skewness," Discussion Paper 1996-58, Tilburg University, Center for Economic Research.
    3. Palmitesta Paola & Provasi Corrado, 2004. "GARCH-type Models with Generalized Secant Hyperbolic Innovations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-19, May.
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    More about this item

    Keywords

    Risk Management; Monte Carlo Method; Generalized Lambda Distribution; Koehler-Symanowski Distribution;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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