Information
- Name: Simon-Pierre Gadoury
- Education: B.Sc. in Actuarial Sciences at Laval University
- Status: M.Sc. Candidate in Quantitative Finance at ETH Zürich
- Curriculum Vitae
LaTeX
- Beamer templates: Private repository
R packages
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erhcv: Equi-Rank Hierarchical Clustering Validation
Assesses the statistical significance of clusters for a given dataset through bootstrapping and hypothesis testing of a given matrix of empirical Spearman’s rho, based on the technique of S. Gaiser et al. (2010).
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nCopula: Hierarchical Archimedean Copulas with Multivariate Compound Distributions
Construct and manipulate hierarchical Archimedean copulas with multivariate compound distributions. The model used is the one of (Cossette et al. (2017)).
Papers
Published
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Hierarchical Archimedean copulas through multivariate compound distributions
In this paper, we propose a new hierarchical Archimedean copula construction based on multivariate compound distributions. This new imbrication technique is derived via the construction of a multivariate exponential mixture distribution through compounding. The absence of nesting and marginal conditions, contrarily to the nested Archimedean copulas approach, leads to major advantages, such as a flexible range of possible combinations in the choice of distributions, the existence of explicit formulas for the distribution of the sum, and computational ease in high dimensions. A balance between flexibility and parsimony is targeted. After presenting the construction technique, properties of the proposed copulas are investigated and illustrative examples are given. A detailed comparison with other construction methodologies of hierarchical Archimedean copulas is provided. Risk aggregation under this newly proposed dependence structure is also examined.
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We consider the family of hierarchical Archimedean copulas whose imbrication technique is derived via the construction of a multivariate exponential mixture distribution through compounding, as introduced in (Cossette et al., 2017). We investigate the structure determination and the estimation of these copulas. An agglomerative clustering technique based on the Spearman’s rho matrix combined with a bootstrap procedure is used to identify the tree structure. The parameter estimation is done through a top-down composite likelihood method. The validity of the proposed approach is illustrated through two simulation studies in which the procedure is explained step by step. The composite likelihood method is also compared to the full likelihood method in a simple case where the full likelihood is computable.