Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility (Forthcoming in European Journal of Operational Research)

Shiraya, Kenichiro; Yamakami, Tomohisa

Constructing Copulas Using Corrected Hermite Polynomial Expansion for Estimating Cross Foreign Exchange Volatility (Forthcoming in European Journal of Operational Research)

Kenichiro Shiraya and Tomohisa Yamakami
Additional contact information
Kenichiro Shiraya: Graduate School of Economics, The University of Tokyo
Tomohisa Yamakami: Graduate School of Economics, The University of Tokyo

No CARF-F-553, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: 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.

Pages: 36
Date: 2023-01
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf553

Access Statistics for this paper

More papers in CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo Contact information at EDIRC.
Bibliographic data for series maintained by ().