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Local Variance Gamma and Explicit Calibration to Option Prices

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  • Peter Carr
  • Sergey Nadtochiy
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    Abstract

    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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    File URL: http://arxiv.org/pdf/1308.2326
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1308.2326.

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    Date of creation: Aug 2013
    Date of revision: Jan 2014
    Handle: RePEc:arx:papers:1308.2326

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    Web page: http://arxiv.org/

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    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 511-24, October.
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