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Goodness-of-fit for regime-switching copula models with application to option pricing
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Journal Article
Goodness-of-fit for regime-switching copula models with application to option pricing
2020
Overview
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.
Les auteurs considèrent plusieurs séries temporelles univariées et trouvent pour chacune un modèle dynamique paramétrique approprié. Ils obtiennent alors des termes d’erreur indépendants pour chaque série et modélisent la dépendance entre ces termes d’erreur par une copule avec changement de régime. Ils utilisent l’algorithme EM pour estimer les paramètres et proposent une procédure séquentielle de tests d’adéquation basés sur la statistique de Cramér-von Mises pour sélectionner le nombre approprié de régimes. Les auteurs réalisent une série d’expériences numériques afin d’évaluer la validité et la performance de la méthodologie proposée. À titre d’exemple d’application, ils évaluent le prix d’une option de vente européenne sur le rendement maximal de deux titres en utilisant un modèle de copule à changement de régime. Finalement, afin de faciliter l’utilisation future de la méthodologie proposée, ils construisent une librairie de fonctions basée sur le progiciel R qui s’intitule HMMcopula et qui est disponible gratuitement sur le CRAN.
Publisher
Wiley,John Wiley & Sons, Inc,Wiley Subscription Services, Inc
Subject
