Local Volatility Pricing Models for Long-Dated FX Derivatives

22 Pages Posted: 14 Jun 2010 Last revised: 3 Apr 2012

See all articles by Griselda Deelstra

Griselda Deelstra

Université Libre de Bruxelles (ULB)

Grégory Rayée

Université Libre de Bruxelles (ULB)

Date Written: June 2, 2010

Abstract

We study the local volatility function in the Foreign Exchange market where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility on the FX option's market. Then, we study two different extensions which allow the volatility of the spot FX rate to have stochastic behavior. First, we introduce a stochastic structure on the local volatility surface and show that local volatilities are risk-adjusted expectations of future instantaneous volatilities. The second extension is obtained by multiplying the FX spot local volatility with a stochastic volatility. Thanks to the Gyöngy's mimicking property, we obtain a calibration method for the local volatility associated to this model.

Keywords: Local volatility, Stochastic volatility, Foreign Exchange,Stochastic interest rates, Calibration

JEL Classification: C00

Suggested Citation

Deelstra, Griselda and Rayée, Grégory, Local Volatility Pricing Models for Long-Dated FX Derivatives (June 2, 2010). Available at SSRN: https://ssrn.com/abstract=1624762 or http://dx.doi.org/10.2139/ssrn.1624762

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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