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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.

Suggested Citation

  • Griselda Deelstra & Gr'egory Ray'ee, 2012. "Local Volatility Pricing Models for Long-dated FX Derivatives," Papers 1204.0633, arXiv.org.
  • Handle: RePEc:arx:papers:1204.0633
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    File URL: http://arxiv.org/pdf/1204.0633
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    References listed on IDEAS

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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. 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.
    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.
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    Cited by:

    1. Maria Cristina Recchioni & Yu Sun & Gabriele Tedeschi, 2016. "Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model," Working Papers 2016/23, Economics Department, Universitat Jaume I, Castellón (Spain).
    2. Recchioni, M.C. & Sun, Y., 2016. "An explicitly solvable Heston model with stochastic interest rate," European Journal of Operational Research, Elsevier, vol. 249(1), pages 359-377.
    3. 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.
    4. 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.
    5. Neeraj J. Gupta & Mark Kurt & Reilly White, 2016. "The Buffett critique: volatility and long-dated options," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 40(3), pages 524-537, July.
    6. Andrei Cozma & Matthieu Mariapragassam & Christoph Reisinger, 2015. "Convergence of an Euler scheme for a hybrid stochastic-local volatility model with stochastic rates in foreign exchange markets," Papers 1501.06084, arXiv.org, revised Oct 2016.

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