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Option Pricing Model Biases: Bayesian and Markov Chain Monte Carlo Regression Analysis

Author

Listed:
  • Sharif Mozumder

    (University of Dhaka)

  • Taufiq Choudhry

    (University of Southampton)

  • Michael Dempsey

    (Ton Duc Thang University)

Abstract

We investigate systematic and unsystematic option pricing biases in (a) pure jump Lévy, (b) jump-diffusion, (c) stochastic volatility, and (d) GARCH models applied to the Black–Scholes–Merton model. We use options data for trades on the S&P500 index from the CBOE. In addition to standard ordinary least square regression, we employ Bayesian regression and Markov Chain Monte Carlo regression to investigate the moneyness and maturity biases of the models. We demonstrate the usefulness of these advanced methodologies as compared to the benchmark techniques.

Suggested Citation

  • Sharif Mozumder & Taufiq Choudhry & Michael Dempsey, 2021. "Option Pricing Model Biases: Bayesian and Markov Chain Monte Carlo Regression Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1287-1305, April.
    • Handle: RePEc:kap:compec:v:57:y:2021:i:4:d:10.1007_s10614-020-10029-x
    DOI: 10.1007/s10614-020-10029-x
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    References listed on IDEAS

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    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Geman, Helyette, 2002. "Pure jump Levy processes for asset price modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1297-1316, July.
    5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    6. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    7. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    8. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," The Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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