Quanto Implied Correlation in a Multi-Lévy Framework

25 Pages Posted: 24 Feb 2015 Last revised: 22 Oct 2015

See all articles by Laura Ballotta

Laura Ballotta

Sir John Cass Business School - City, University of London

Griselda Deelstra

Université Libre de Bruxelles (ULB)

Grégory Rayée

Université Libre de Bruxelles (ULB)

Date Written: October 20, 2015

Abstract

In this paper we apply the multivariate construction for Lévy processes introduced by Ballotta and Bonfiglioli (2014) to propose an integrated model for the joint dynamics of FX exchange rates and asset prices. We show that the proposed construction is consistent in terms of symmetries with respect to inversion and triangulation, and provides an insight into the quanto adjustment showing that this is affected by higher order cumulants of the pure jump part of the systematic risk factor. Using the Esscher transform, we relate Quanto options to vanilla call and put options, which allows for a fast calibration method to the vanilla and the Quanto market. As Quanto products offer significant exposure to the correlation between exchange rates and asset prices, they allow access to a market implied measure of this correlation. By means of a joint calibration exercise to the CME USD denominated Quanto futures on the Nikkei 225 index and both the Nikkei 225 and USDJPY market implied volatilities, we illustrate this approach for the case in which the driving process is assumed to be a Variance Gamma process.

Keywords: FX risk, implied correlation, multivariate Lévy processes, Quanto products, triangular relation, Variance Gamma process

JEL Classification: G13, G12, C63, D52

Suggested Citation

Ballotta, Laura and Deelstra, Griselda and Rayée, Grégory, Quanto Implied Correlation in a Multi-Lévy Framework (October 20, 2015). Available at SSRN: https://ssrn.com/abstract=2569015 or http://dx.doi.org/10.2139/ssrn.2569015

Laura Ballotta

Sir John Cass Business School - City, University of London ( email )

Faculty of Finance
106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

HOME PAGE: http://www.city.ac.uk/people/academics/laura-ballotta

Griselda Deelstra

Université Libre de Bruxelles (ULB) ( email )

Boulevard du Triomphe, CP210
Brussels, Brussels 1050
Belgium

Grégory Rayée (Contact Author)

Université Libre de Bruxelles (ULB) ( email )

CP 114/04 Av FD Roosevelt 50
Brussels, 1050
Belgium

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