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An Autoregressive Conditional Binomial Option Pricing Model

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  • Jean -Luc Prigent

    (Crest)

  • Olivier Renault

    (Crest)

  • Olivier Scaillet

    (Crest)

Abstract

This paper offers an option pricing framework grounded in econometric microstructure modelling. We consider a model where stock price dynamics follow a pure jump process with constant jump size similar to a binomial setting with random time steps. Jump arrival times are described as an Autoregressive Conditional Duration (ACD) process while conditional probabilities of up-moves and down-moves are given by the logistic transformation of an autoregressive prices. We derive no-arbitrage pricing formulae under the minimal martingale measure and illustrate the use of our Autoregressive Conditional Binomial (ACB) option pricing model on intraday IBM stock date.
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Suggested Citation

  • Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:99-65
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    Cited by:

    1. J.L. Prigent & O. Scaillet, 2000. "Weak Convergence of Hedging Strategies of Contingent Claims," THEMA Working Papers 2000-50, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
    3. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    4. Pierre Giot, 2005. "Market risk models for intraday data," The European Journal of Finance, Taylor & Francis Journals, vol. 11(4), pages 309-324.
    5. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    6. Maria Pacurar, 2008. "Autoregressive Conditional Duration Models In Finance: A Survey Of The Theoretical And Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 711-751, September.
    7. GIOT, Pierre, 2000. "Intraday value-at-risk," CORE Discussion Papers 2000045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Hujer, Reinhard & Vuletic, Sandra, 2007. "Econometric analysis of financial trade processes by discrete mixture duration models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 635-667, February.
    9. Pipat Wongsaart & Jiti Gao, 2011. "Nonparametric Kernel Testing in Semiparametric Autoregressive Conditional Duration Model," Monash Econometrics and Business Statistics Working Papers 18/11, Monash University, Department of Econometrics and Business Statistics.
    10. Damiano Brigo & Francesco Rapisarda & Abir Sridi, 2013. "The arbitrage-free Multivariate Mixture Dynamics Model: Consistent single-assets and index volatility smiles," Papers 1302.7010, arXiv.org, revised Sep 2014.

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