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Discrete versus continuous time models: Local martingales and singular processes in asset pricing theory

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  • Jarrow, Robert
  • Protter, Philip

Abstract

In economic theory, both discrete and continuous time models are commonly believed to be equivalent in the sense that one can always be used to approximate the other, or equivalently, any phenomena present in one is also present in the other. This common belief is misguided. Both (strict) local martingales and singular processes exist in continuous time, but not in discrete time models. More importantly, their existence reflects real economic phenomena related to arbitrage opportunities, large traders, asset price bubbles, and market efficiency. And as an approximation to trading opportunities in real markets, continuous trading provides a better fit and should be the preferred modeling approach for asset pricing theory.

Suggested Citation

  • Jarrow, Robert & Protter, Philip, 2012. "Discrete versus continuous time models: Local martingales and singular processes in asset pricing theory," Finance Research Letters, Elsevier, vol. 9(2), pages 58-62.
    • Handle: RePEc:eee:finlet:v:9:y:2012:i:2:p:58-62
    DOI: 10.1016/j.frl.2012.03.002
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    Cited by:

    1. Alexander M. G. Cox & Zhaoxu Hou & Jan Obloj, 2014. "Robust pricing and hedging under trading restrictions and the emergence of local martingale models," Papers 1406.0551, arXiv.org, revised Jun 2015.
    2. Oksana Bashchenko & Alexis Marchal, 2020. "Deep Learning for Asset Bubbles Detection," Papers 2002.06405, arXiv.org.

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    More about this item

    Keywords

    Local martingales; Singular processes; Arbitrage opportunities; Large traders; Asset price bubbles; Market efficiency;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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