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Local Volatility Pricing Models for Long-dated FX Derivatives

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  • Griselda Deelstra
  • Gr\'egory Ray\'ee

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 an extension to obtain a more general volatility model and propose a calibration method for the local volatility associated to this model.

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File URL: http://arxiv.org/pdf/1204.0633
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1204.0633.

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Date of creation: Apr 2012
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Handle: RePEc:arx:papers:1204.0633

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  1. 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.
  2. 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.
  3. Lech A. Grzelak & Cornelis W. Oosterlee, 2012. "On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 1-35, February.
  4. 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.
  5. 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.
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Cited by:
  1. Deelstra, Griselda & Rayée, Grégory, 2013. "Pricing Variable Annuity Guarantees in a local volatility framework," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 650-663.
  2. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.

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