Goodness-of-fit for regime-switching copula models with application to option pricing |
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Authors: | Bouchra R. Nasri Bruno N. Rémillard Mamadou Y. Thioub |
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Affiliation: | 1. Department of Mathematics and Statistics, McGill University, 805 Rue Sherbrooke O, Montréal, Québec, Canada, H3A 0B9;2. Department of Decision Sciences, HEC Montréal, 3000 chemin de la Côte-Sainte-Catherine, Montréal, Québec, H3T 2A7 |
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Abstract: | We consider several time series, and for each of them, we fit an appropriate dynamic parametric model. This produces serially independent error terms for each time series. The dependence between these error terms is then modelled by a regime-switching copula. The EM algorithm is used for estimating the parameters and a sequential goodness-of-fit procedure based on Cramér–von Mises statistics is proposed to select the appropriate number of regimes. Numerical experiments are performed to assess the validity of the proposed methodology. As an example of application, we evaluate a European put-on-max option on the returns of two assets. To facilitate the use of our methodology, we have built a R package HMMcopula available on CRAN. The Canadian Journal of Statistics 48: 79–96; 2020 © 2020 Statistical Society of Canada |
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Keywords: | Copulas generalized error models goodness-of-fit regime-switching models time series |
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