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An Autoregressive Conditional Binomial Option Pricing Model

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  • Olivier Renault
  • Jean-Luc Prigent
  • Olivier Scaillet

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.

Suggested Citation

  • Olivier Renault & Jean-Luc Prigent & Olivier Scaillet, 2000. "An Autoregressive Conditional Binomial Option Pricing Model," FMG Discussion Papers dp364, Financial Markets Group.
    • Handle: RePEc:fmg:fmgdps:dp364
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    References listed on IDEAS

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    Citations

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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, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    4. GIOT, Pierre, 2000. "Intraday value-at-risk," LIDAM Discussion Papers CORE 2000045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. 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.
    7. 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.
    8. Prigent, Jean-Luc & Renault, Olivier & Scaillet, Olivier, 2004. "Option pricing with discrete rebalancing," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 133-161, January.
    9. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    10. Pierre Giot, 2005. "Market risk models for intraday data," The European Journal of Finance, Taylor & Francis Journals, vol. 11(4), pages 309-324.
    11. repec:bla:jecsur:v:22:y:2008:i:4:p:711-751 is not listed on IDEAS

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    More about this item

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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