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Option pricing with Levy Process

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  • Eric Benhamou

    (Goldman Sachs International)

Abstract

In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristics of the Levy process from option prices. This enables us to generate an implicit volatility surface implied by market data. This model is of particular interest since it extends the seminal Black Scholes [1973] model consistently with volatility smile.

Suggested Citation

  • Eric Benhamou, 2002. "Option pricing with Levy Process," Finance 0212006, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0212006
    Note: Type of Document - PDF; prepared on windows; pages: 118
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    References listed on IDEAS

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    Cited by:

    1. Eric Benhamou & David Saltiel & Serge Tabachnik & Sui Kai Wong & François Chareyron, 2021. "Distinguish the indistinguishable: a Deep Reinforcement Learning approach for volatility targeting models," Working Papers hal-03202431, HAL.
    2. Leif Andersen & Alexander Lipton, 2013. "Asymptotics For Exponential Lévy Processes And Their Volatility Smile: Survey And New Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-98.
    3. Kais Hamza & Fima C. Klebaner & Zinoviy Landsman & Ying-Oon Tan, 2014. "Option Pricing for Symmetric L\'evy Returns with Applications," Papers 1402.1554, arXiv.org.
    4. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
    5. Jaimungal, Sebastian & Young, Virginia R., 2005. "Pricing equity-linked pure endowments with risky assets that follow Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 329-346, June.
    6. Evis Këllezi & Nick Webber, 2004. "Valuing Bermudan options when asset returns are Levy processes," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 87-100.

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    More about this item

    Keywords

    Levy process; Fourier and Laplace transform; Smile.;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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