An Affine Multi-Currency Model with Stochastic Volatility and Stochastic Interest Rates

SIAM Journal on Financial Mathematics, Forthcoming

43 Pages Posted: 1 Mar 2013 Last revised: 7 May 2014

See all articles by Alessandro Gnoatto

Alessandro Gnoatto

University of Verona - Department of Economics

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Date Written: May 07, 2014

Abstract

We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed efficiently through the FFT methodology thanks to the affinity of the model. A joint calibration exercise of the implied volatility surfaces of a triangle of FX rates shows the flexibility of our framework in dealing with the typical symmetries that characterize the FX market. Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the ability of the model to fi t simultaneously FX implied volatilities while being coherent with interest rate products.

Keywords: FX options, Hybrid models, longdated FX, Wishart process, Affine process, FFT

JEL Classification: G130, G120, G150

Suggested Citation

Gnoatto, Alessandro and Grasselli, Martino, An Affine Multi-Currency Model with Stochastic Volatility and Stochastic Interest Rates (May 07, 2014). SIAM Journal on Financial Mathematics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2226499 or http://dx.doi.org/10.2139/ssrn.2226499

Alessandro Gnoatto (Contact Author)

University of Verona - Department of Economics ( email )

Via dell'Artigliere, 8
37129 Verona
Italy

Martino Grasselli

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

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