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An Implementation of Bouchouev's Method for a Short Time Calibration of Option Pricing Models

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  • Carl Chiarella
  • Mark Craddock
  • Nadima El-Hassan

Abstract

We analyse the Bouchouev integral equation for the deterministic volatility function in the Black–Scholes option pricing model. We areable to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Carl Chiarella & Mark Craddock & Nadima El-Hassan, 2003. "An Implementation of Bouchouev's Method for a Short Time Calibration of Option Pricing Models," Computational Economics, Springer;Society for Computational Economics, vol. 22(2), pages 113-138, October.
    • Handle: RePEc:kap:compec:v:22:y:2003:i:2:p:113-138
    DOI: 10.1023/A:1026177612385
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    References listed on IDEAS

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    1. 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.
    2. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    3. Carl Chiarella & Mark Craddock & Nadima El-Hassan, 2000. "The Calibration of Stock Option Pricing Models Using Inverse Problem Methodology," Research Paper Series 39, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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    Cited by:

    1. Carl Chiarella & Mark Craddock & Nadima El-Hassan, 2000. "The Calibration of Stock Option Pricing Models Using Inverse Problem Methodology," Research Paper Series 39, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Philippe Jacquinot & Nikolay Sukhomlin, 2010. "A direct formulation of implied volatility in the Black-Scholes model," Post-Print hal-02533014, HAL.
    3. Philippe Jacquinot & Nikolay Sukhomlin, 2010. "A direct formulation of implied volatility in the Black- Scholes model," Post-Print hal-02527822, HAL.

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