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Dupire’s formulas in the Piterbarg option pricing model

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  • Labuschagne, Coenraad C.A.
  • von Boetticher, Sven T.

Abstract

In this paper we derive an expression for the local volatility of an underlying asset, given the prices of liquid European call options under the Piterbarg framework. The Piterbarg framework is a multi-curve derivative pricing model which extends the well known Black–Scholes–Merton model by relaxing the assumption of a risk-free interest rate, and includes collateral payments. The expressions for the local volatility is a function of the option price surface, and is then transformed to become a function of the implied volatility surface.

Suggested Citation

  • Labuschagne, Coenraad C.A. & von Boetticher, Sven T., 2016. "Dupire’s formulas in the Piterbarg option pricing model," The North American Journal of Economics and Finance, Elsevier, vol. 38(C), pages 148-162.
    • Handle: RePEc:eee:ecofin:v:38:y:2016:i:c:p:148-162
    DOI: 10.1016/j.najef.2016.09.002
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    References listed on IDEAS

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    1. Damiano Brigo & Fabio Mercurio, 2002. "Lognormal-Mixture Dynamics And Calibration To Market Volatility Smiles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 427-446.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Chen, Ren-Raw & Leistikow, Dean & Wang, Andrew, 2020. "Futures minimum variance hedge ratio determination: An ex-ante analysis," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).

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