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A parsimonious model for intraday European option pricing

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  • Scalas, Enrico
  • Politi, Mauro

Abstract

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools.

Suggested Citation

  • Scalas, Enrico & Politi, Mauro, 2012. "A parsimonious model for intraday European option pricing," Economics Discussion Papers 2012-14, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwedp:201214
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    References listed on IDEAS

    as
    1. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    2. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    3. Engle, Robert F. & Russell, Jeffrey R., 1997. "Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 187-212, June.
    4. Toke, Ioane Muni & Pomponio, Fabrizio, 2011. "Modelling trades-through in a limited order book using Hawkes processes," Economics Discussion Papers 2011-32, Kiel Institute for the World Economy (IfW Kiel).
    5. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    6. Enrico Scalas, 2011. "A class of CTRWs: Compound fractional Poisson processes," Papers 1103.0647, arXiv.org.
    7. Scalas, Enrico, 2007. "Mixtures of compound Poisson processes as models of tick-by-tick financial data," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 33-40.
    8. Álvaro Cartea, 2013. "Derivatives pricing with marked point processes using tick-by-tick data," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
    9. Meerschaert, Mark M. & Scalas, Enrico, 2006. "Coupled continuous time random walks in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 114-118.
    10. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    11. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    12. M. Montero, 2008. "Renewal equations for option pricing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(2), pages 295-306, September.
    13. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    14. Gerald Cheang & Carl Chiarella, 2011. "A Modern View on Merton's Jump-Diffusion Model," Research Paper Series 287, Quantitative Finance Research Centre, University of Technology, Sydney.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Option pricing; high-frequency finance; high-frequency trading; computer trading; jump-diffusion models; pure-jump models; continuous time random walks; semi-Markov processes;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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