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Local Volatility Calibration Using An Adjoint Proxy

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  • Gabriel TURINICI

    (CEREMADE, Université Paris Dauphine)

Abstract

We document the calibration of the local volatility in a framework similar to Coleman, Li and Verma. The quality of a surface is assessed through a functional to be optimized; the specificity of the approach is to separate the optimization (performed with any suitable optimization algorithm) from the computation of the functional where we use an adjoint (as in L. Jiang et. al.) to obtain an approximation; moreover our main calibration variable is the implied volatility (the procedure can also accommodate the Greeks). The procedure performs well on benchmarks from the literature and on FOREX data.

Suggested Citation

  • Gabriel TURINICI, 2008. "Local Volatility Calibration Using An Adjoint Proxy," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 2, pages 93-105, November.
    • Handle: RePEc:aic:revebs:y:2008:i:2:turinicig
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    References listed on IDEAS

    as
    1. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    2. Ronald Lagnado & Stanley Osher, "undated". "A Technique for Calibrating Derivative Security Pricing Models: Numerical Solution of an Inverse Problem," Computing in Economics and Finance 1997 101, Society for Computational Economics.
    3. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    4. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    5. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    6. Lishang Jiang & Qihong Chen & Lijun Wang & Jin Zhang, 2003. "A new well-posed algorithm to recover implied local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 451-457.
    7. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    8. 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.
    9. Thomas F. Coleman & Yuying Li & Arun Verma, 2001. "Reconstructing The Unknown Local Volatility Function," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 7, pages 192-215, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Gabriel Turinici, 2009. "Robust recovery of the risk neutral probability density from option prices," Analele Stiintifice ale Universitatii "Alexandru Ioan Cuza" din Iasi - Stiinte Economice (1954-2015), Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, vol. 56, pages 197-201, November.

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