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On the consistency of jump-diffusion dynamics for FX rates under inversion

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  • Federico Graceffa

    (Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK)

  • Damiano Brigo

    (Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK)

  • Andrea Pallavicini

    (#x2020;Department of Mathematics, Imperial College London, Banca IMI Milan, Largo Mattioli 3, Milan MI 20121, Italy)

Abstract

We investigate the consistency under inversion of jump diffusion processes in the foreign exchange market. That is, if the EUR/USD exchange rate follows a given type of dynamics, under which conditions will USD/EUR follow the same type of dynamics? After giving a numerical description of this property, we establish a suitable local volatility structure ensuring consistency. We subsequently introduce jumps and analyze both constant and random jump size. While in the first scenario consistency is automatically satisfied, the second case is more involved. A fairly general class of admissible densities for the jump size in the domestic measure is determined.

Suggested Citation

  • Federico Graceffa & Damiano Brigo & Andrea Pallavicini, 2020. "On the consistency of jump-diffusion dynamics for FX rates under inversion," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 1-17, December.
    • Handle: RePEc:wsi:ijfexx:v:07:y:2020:i:04:n:s2424786320500462
    DOI: 10.1142/S2424786320500462
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    References listed on IDEAS

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    1. Damiano Brigo & Nicola Pede & Andrea Petrelli, 2019. "Multi-Currency Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-35, June.
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    Cited by:

    1. 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.

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