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Expansion Formulas For European Quanto Options In A Local Volatility Fx-Libor Model

Author

Listed:
  • JULIEN HOK

    (Credit Agricole CIB, Broadwalk House, 5 Appold St, EC2A 2DA London, UK)

  • PHILIP NGARE

    (#x2020;School of Mathematics, University of Nairobi, P.O. Box 30197-0010, Nairobi, Kenya)

  • ANTONIS PAPAPANTOLEON

    (#x2021;Department of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, Greece)

Abstract

We develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the price of the quanto option. In order to take the skew/smile effect observed in fixed income and FX markets into account, we consider local volatility models for both the LIBOR and the FX rate. Because of the structure of the local volatility function, a closed form solution for quanto option prices does not exist. Using expansions around a proxy related to log-normal dynamics, we derive approximation formulas of Black–Scholes type for the price, that have the benefit of giving very rapid numerical procedures. Our expansion formulas have the major advantage that they allow for an accurate estimation of the error, using Malliavin calculus, which is directly related to the maturity of the option, the payoff, and the level and curvature of the local volatility function. These expansions also illustrate the impact of the quanto drift adjustment, while the numerical experiments show an excellent accuracy.

Suggested Citation

  • Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion Formulas For European Quanto Options In A Local Volatility Fx-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-43, March.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:02:n:s0219024918500176
    DOI: 10.1142/S0219024918500176
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Umut Çetin & Julien Hok, 2024. "Speeding up the Euler scheme for killed diffusions," Finance and Stochastics, Springer, vol. 28(3), pages 663-707, July.
    3. Cetin, Umut & Hok, Julien, 2024. "Speeding up the Euler scheme for killed diffusions," LSE Research Online Documents on Economics 120789, London School of Economics and Political Science, LSE Library.
    4. George Hong, 2020. "Skewing Quanto with Simplicity," Papers 2009.02566, arXiv.org.

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