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

Paola Palmitesta and Corrado Provasi

No 306, Computing in Economics and Finance 2004 from Society for Computational Economics

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

Keywords: Risk Management; Monte Carlo Method; Generalized Lambda Distribution; Koehler-Symanowski Distribution (search for similar items in EconPapers)
JEL-codes: C15 C16 C63 (search for similar items in EconPapers)
Date: 2004-08-11
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