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An analytic multi-currency model with stochastic volatility and stochastic interest rates

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  • Alessandro Gnoatto
  • Martino Grasselli

Abstract

We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinity of the model Our framework is also able to describe many non trivial links between FX rates and interest rates: a second calibration exercise highlights the ability of the model to fit simultaneously FX implied volatilities while being coherent with interest rate products.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1302.7246
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    Cited by:

    1. Matthias Muck, 2022. "Arbitrage-free smile construction on FX option markets using Garman-Kohlhagen deltas and implied volatilities," Review of Derivatives Research, Springer, vol. 25(3), pages 293-314, October.
    2. Branger, Nicole & Herold, Michael & Muck, Matthias, 2021. "International stochastic discount factors and covariance risk," Journal of Banking & Finance, Elsevier, vol. 123(C).
    3. Alessandro Gnoatto, 2017. "Coherent Foreign Exchange Market Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-29, February.
    4. Alessandro Gnoatto & Martino Grasselli & Eckhard Platen, 2016. "A Penny Saved is a Penny Earned: Less Expensive Zero Coupon Bonds," Papers 1608.04683, arXiv.org, revised Mar 2018.
    5. Akihiko Takahashi, 2015. "Asymptotic Expansion Approach in Finance," CARF F-Series CARF-F-356, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Aug 2015.
    6. Fazlollah Soleymani & Andrey Itkin, 2019. "Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method," Papers 1903.00937, arXiv.org.
    7. Shunwei Zhu & Bo Wang, 2019. "Unified Approach for the Affine and Non-affine Models: An Empirical Analysis on the S&P 500 Volatility Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1421-1442, April.

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