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The Calibration of Stock Option Pricing Models Using Inverse Problem Methodology

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Abstract

We analyse the procedure for determining volatility presented by Lagnado and Osher, and explain in some detail where the scheme comes from. We present an alternative scheme which avoids some of the technical complications arising in Lagnado and Osher's approach. An algorithm for solving the resulting equations is given, along with a selection of numerical examples.

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  • 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.
    • Handle: RePEc:uts:rpaper:39
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    1. 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.
    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. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    4. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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    1. Yu-Hua Zeng & Shou-Lei Wang & Yu-Fei Yang, 2014. "Calibration of the Volatility in Option Pricing Using the Total Variation Regularization," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, March.
    2. Martin Tegn'er & Stephen Roberts, 2019. "A Probabilistic Approach to Nonparametric Local Volatility," Papers 1901.06021, arXiv.org, revised Jan 2019.
    3. Andrea De Martino & Edward Manuel Ruiz Crosby & Roberto Stagni, 2017. "A unified framework for pricing credit and equity derivatives," Working Papers 116, Peruvian Economic Association.
    4. M. Papi & L. Pontecorvi & C. Donatucci, 2017. "Weighted average price in the Heston stochastic volatility model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 351-373, November.
    5. Shou-Lei Wang & Yu-Fei Yang & Yu-Hua Zeng, 2014. "The Adjoint Method for the Inverse Problem of Option Pricing," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, March.
    6. Tarik Chakkour & Emmanuel Frénod, 2016. "Inverse problem and concentration method of a continuous-in-time financial model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 1-20, June.
    7. Martin Tegner & Stephen Roberts, 2021. "A Bayesian take on option pricing with Gaussian processes," Papers 2112.03718, arXiv.org.
    8. 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.
    9. Vipul Kumar Singh, 2013. "Effectiveness of volatility models in option pricing: evidence from recent financial upheavals," Journal of Advances in Management Research, Emerald Group Publishing Limited, vol. 10(3), pages 352-375, October.

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