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Expansion Formulas For Bivariate Payoffs With Application To Best-Of Options On Equity And Inflation

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  • EMMANUEL GOBET

    (Centre de Mathématiques Appliquées, Ecole Polytechnique and CNRS, Route de Saclay, 91128 Palaiseau Cedex, France)

  • JULIEN HOK

    (Markit, Ropemaker Place 25 Ropemaker Street, London, EC2Y 9LY, United Kingdom)

Abstract

A wide class of hybrid products are evaluated with a model where one of the underlying price follows a local volatility diffusion and the other asset value a log-normal process. Because of the generality for the local volatility function, the numerical pricing is usually much time consuming. Using proxy approximations related to log-normal modeling, we derive approximation formulas of Black–Scholes type for the price, that have the advantage of giving very rapid numerical procedures. This derivation is illustrated with the best-of option between equity and inflation where the stock price follows a local volatility model and the inflation rate a Hull–White process. The approximations possibly account for Gaussian HJM (Heath-Jarrow-Morton) models for interest rates. The experiments show an excellent accuracy.

Suggested Citation

  • Emmanuel Gobet & Julien Hok, 2014. "Expansion Formulas For Bivariate Payoffs With Application To Best-Of Options On Equity And Inflation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-32.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:02:n:s0219024914500101
    DOI: 10.1142/S0219024914500101
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    References listed on IDEAS

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    1. Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Post-Print halshs-03331510, HAL.
    2. Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Cahiers de la Maison des Sciences Economiques b04050, Université Panthéon-Sorbonne (Paris 1).
    3. Nabyl Belgrade & Eric Benhamou & Etienne Koehler, 2004. "A market model for inflation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03331510, HAL.
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    Cited by:

    1. Colin Turfus & Alexander Shubert, 2017. "ANALYTIC PRICING OF CoCo BONDS," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-26, August.
    2. 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.
    3. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion formulas for European quanto options in a local volatility FX-LIBOR model," Papers 1801.01205, arXiv.org, revised Apr 2018.
    4. 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.

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