A new copula for modeling portfolios with skewed, leptokurtic and high-order dependent risk factors

Quatto, Piero; Vacca, Gianmarco; Zoia, Maria Grazia

doi:10.1016/j.najef.2021.101529

Cited by 5 publications

(1 citation statement)

References 34 publications

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“…This point has not been resolved in these studies. Quatto et al [16] have proposed a constraint on the coefficients of the fourth-order multivariate Hermite polynomial expansion. While it satisfies the copula's condition, the constraint is very strong and difficult to apply to a variety of issues.…”

Section: Introductionmentioning

confidence: 99%

Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility

Shiraya¹,

Yamakami²

2023

Preprint

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Copulas are used to construct joint distributions in many areas. In some problems, it is necessary to deal with correlation structures that are more complicated than the commonly known copulas. A finite order multivariate Hermite polynomial expansion, as an approximation of a joint density function, can handle complex correlation structures. However, it does not construct copulas because the density function can take negative values. In this study, we propose a method to construct a copula based on the finite sum of multivariate Hermite polynomial expansions by applying corrections to the joint density function.Furthermore, we apply this copula to estimate the volatility smile of cross currency pairs in the foreign exchange option market. This method can easily reproduce the volatility smile of cross currency pairs by appropriately adjusting the parameters and following the daily volatility fluctuations even if the higher-order parameters are fixed. In the numerical experiments, we compare the estimation results of the volatility smile of EUR-JPY with those of USD-JPY and EUR-USD for the proposed and other copulas, and show the validity of the proposed copula.

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Section: Introductionmentioning

confidence: 99%