Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility

Kenichiro Shiraya and Tomohisa Yamakami

European Journal of Operational Research, 2024, vol. 314, issue 3, 1195-1214

Abstract: 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 formulation of multivariate Hermite polynomial expansion suitable for the application of correction that recovers non-negativity and construct a copula. Several useful expressions for integrals with the copula are derived from this formulation. We also apply this copula to estimate the volatility smile of cross-currency pairs in the foreign exchange option market. In the numerical experiments, we compare the estimation results of the volatility smile of EUR–JPY, GBP–JPY, and AUD–JPY for the proposed and other copulas to confirm the validity of the proposed copula.

Keywords: Finance; Copula; Hermite polynomial expansion; Currency option; Correction of probability density (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:314:y:2024:i:3:p:1195-1214

DOI: 10.1016/j.ejor.2023.11.033

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