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Coherent Foreign Exchange Market Models

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  • ALESSANDRO GNOATTO

    (Mathematisches Institut der LMU München, Theresienstrasse, 39 D-80333 München, Germany)

Abstract

A model describing the dynamics of a foreign exchange (FX) rate should preserve the same level of analytical tractability when the inverted FX process is considered. We show that affine stochastic volatility models satisfy such a requirement. Such a finding allows us to use affine stochastic volatility models as a building block for FX dynamics that are functionally-invariant with respect to the construction of suitable products/ratios of rates, thus generalizing the model of [A. De Col, A. Gnoatto & M. Grasselli (2013) Smiles all around: FX joint calibration in a multi-Heston model, Journal of Banking and Finance 37 (10), 3799–3818.].

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:01:n:s0219024917500078
    DOI: 10.1142/S0219024917500078
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    References listed on IDEAS

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    Cited by:

    1. Alessandro Gnoatto & Martino Grasselli & Eckhard Platen, 2022. "Calibration to FX triangles of the 4/2 model under the benchmark approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 1-34, June.
    2. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2021. "CBI-time-changed L\'evy processes for multi-currency modeling," Papers 2112.02440, arXiv.org, revised Jul 2022.
    3. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2024. "CBI-time-changed Lévy processes for multi-currency modeling," Annals of Operations Research, Springer, vol. 336(1), pages 127-152, May.

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