Local Volatility Pricing Models for Long-dated FX Derivatives
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 an extension to obtain a more general volatility model and propose a calibration method for the local volatility associated to this model.
References listed on IDEAS
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- Frédéric Bossens & Grégory Rayée & Nikos S. Skantzos & Griselda Deelstra, 2010.
"Vanna-Volga Methods Applied To Fx Derivatives: From Theory To Market Practice,"
International Journal of Theoretical and Applied Finance (IJTAF),
World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1293-1324.
- Fr\'ed\'eric Bossens & Gr\'egory Ray\'ee & Nikos S. Skantzos & Griselda Deelstra, 2009. "Vanna-Volga methods applied to FX derivatives : from theory to market practice," Papers 0904.1074, arXiv.org, revised May 2010.
- Rehez Ahlip, 2008. "Foreign Exchange Options Under Stochastic Volatility And Stochastic Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(03), pages 277-294.
- Grzelak, Lech & Oosterlee, Kees, 2010.
"On cross-currency models with stochastic volatility and correlated interest rates,"
23020, University Library of Munich, Germany.
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- Hull, John & White, Alan, 1993. "One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(02), pages 235-254, June.
- Alexander van Haastrecht & Antoon Pelsser, 2011. "Generic pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 665-691.
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