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Vanna-Volga Methods Applied To Fx Derivatives: From Theory To Market Practice

Author

Listed:
  • FRÉDÉRIC BOSSENS

    (Termeulenstraat 86A, Sint-Genesius-Rode, B-1640, Belgium)

  • GRÉGORY RAYÉE

    (Solvay Brussels School of Economics and Management, Université Libre de Bruxelles, Avenue FD Roosevelt 50, CP 165, Brussels 1050, Belgium)

  • NIKOS S. SKANTZOS

    (Ijzerenmolenstraat 113, Leuven B-3001, Belgium)

  • GRISELDA DEELSTRA

    (Department of Mathematics, Université Libre de Bruxelles, Boulevard du Triomphe, CP 210, Brussels 1050, Belgium)

Abstract

We study Vanna-Volga methods which are used to price first generation exotic options in the Foreign Exchange market. They are based on a rescaling of the correction to the Black–Scholes price through the so-called "probability of survival" and the "expected first exit time". Since the methods rely heavily on the appropriate treatment of market data we also provide a summary of the relevant conventions. We offer a justification of the core technique for the case of vanilla options and show how to adapt it to the pricing of exotic options. Our results are compared to a large collection of indicative market prices and to more sophisticated models. Finally we propose a simple calibration method based on one-touch prices that allows the Vanna-Volga results to be in line with our pool of market data.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:08:n:s0219024910006212
    DOI: 10.1142/S0219024910006212
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    References listed on IDEAS

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    1. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Ballotta, Laura & Deelstra, Griselda & Rayée, Grégory, 2017. "Multivariate FX models with jumps: Triangles, Quantos and implied correlation," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1181-1199.
    2. Markus Hertrich, 2022. "Foreign exchange interventions under a minimum exchange rate regime and the Swiss franc," Review of International Economics, Wiley Blackwell, vol. 30(2), pages 450-489, May.
    3. J. Mart'in Ovejero, 2022. "Vanna-Volga pricing for single and double barrier FX options," Papers 2211.12652, arXiv.org, revised Nov 2022.
    4. Markus Hertrich & Heinz Zimmermann, 2017. "On the Credibility of the Euro/Swiss Franc Floor: A Financial Market Perspective," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(2-3), pages 567-578, March.
    5. Hertrich Markus, 2016. "The Costs of Implementing a Unilateral One-Sided Exchange Rate Target Zone," Review of Economics, De Gruyter, vol. 67(1), pages 91-120, May.
    6. Markus Hertrich, 2015. "A Cautionary Note on the Put-Call Parity under an Asset Pricing Model with a Lower Reflecting Barrier," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 151(III), pages 227-260, September.
    7. Sonali Jain & Jayanth R. Varma & Sobhesh Kumar Agarwalla, 2019. "Indian equity options: Smile, risk premiums, and efficiency," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(2), pages 150-163, February.
    8. Griselda Deelstra & Gr�gory Ray�e, 2013. "Local Volatility Pricing Models for Long-Dated FX Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 380-402, September.
    9. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    10. Hertrich, Markus, 2020. "Foreign exchange interventions under a one-sided target zone regime and the Swiss franc," Discussion Papers 21/2020, Deutsche Bundesbank.

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