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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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    1. 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.
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    Cited by:

    1. Emanuele Nastasi & Andrea Pallavicini & Giulio Sartorelli, 2020. "Smile Modeling In Commodity Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-28, May.
    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. Orcan Ogetbil & Narayan Ganesan & Bernhard Hientzsch, 2020. "Calibrating Local Volatility Models with Stochastic Drift and Diffusion," Papers 2009.14764, arXiv.org, revised May 2023.
    4. Simonella, Roberta & Vázquez, Carlos, 2023. "XVA in a multi-currency setting with stochastic foreign exchange rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 59-79.
    5. 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.
    6. Maria Cristina Recchioni & Yu Sun & Gabriele Tedeschi, 2017. "Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 17(8), pages 1257-1275, August.
    7. Julien Hok & Shih-Hau Tan, 2019. "Calibration of local volatility model with stochastic interest rates by efficient numerical PDE methods," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 609-637, December.
    8. 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.
    9. Olivier Deloire & Louis Roth, 2024. "Multi-asset and generalised Local Volatility. An efficient implementation," Papers 2411.05425, arXiv.org.
    10. 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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