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Local Variance Gamma and Explicit Calibration to Option Prices


  • Peter Carr
  • Sergey Nadtochiy


In some options markets (e.g. commodities), options are listed with only a single maturity for each underlying. In others, (e.g. equities, currencies), options are listed with multiple maturities. In this paper, we provide an algorithm for calibrating a pure jump Markov martingale model to match the market prices of European options of multiple strikes and maturities. This algorithm only requires solutions of several one-dimensional root-search problems, as well as application of elementary functions. We show how to construct a time-homogeneous process which meets a single smile, and a piecewise time-homogeneous process which can meet multiple smiles.

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  • Peter Carr & Sergey Nadtochiy, 2013. "Local Variance Gamma and Explicit Calibration to Option Prices," Papers 1308.2326,, revised Jan 2014.
  • Handle: RePEc:arx:papers:1308.2326

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    References listed on IDEAS

    1. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    2. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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    Cited by:

    1. Noble, John M., 2015. "Time homogeneous diffusion with drift and killing to meet a given marginal," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1500-1540.

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