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On the existence of sure profits via flash strategies

Author

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  • Claudio Fontana
  • Markus Pelger
  • Eckhard Platen

Abstract

We introduce and study the notion of sure profit via flash strategy, consisting of a high-frequency limit of buy-and-hold trading strategies. In a fully general setting, without imposing any semimartingale restriction, we prove that there are no sure profits via flash strategies if and only if asset prices do not exhibit predictable jumps. This result relies on the general theory of processes and provides the most general formulation of the well-known fact that, in an arbitrage-free financial market, asset prices (including dividends) should not exhibit jumps of a predictable direction or magnitude at predictable times. We furthermore show that any price process is always right-continuous in the absence of sure profits. Our results are robust under small transaction costs and imply that, under minimal assumptions, price changes occurring at scheduled dates should only be due to unanticipated information releases.

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  • Claudio Fontana & Markus Pelger & Eckhard Platen, 2017. "On the existence of sure profits via flash strategies," Papers 1708.03099, arXiv.org, revised Jul 2019.
    • Handle: RePEc:arx:papers:1708.03099
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    References listed on IDEAS

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    Cited by:

    1. Claudio Fontana & Zorana Grbac & Sandrine Gümbel & Thorsten Schmidt, 2020. "Term structure modelling for multiple curves with stochastic discontinuities," Finance and Stochastics, Springer, vol. 24(2), pages 465-511, April.
    2. Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Papers 2202.00929, arXiv.org, revised Aug 2023.
    3. Claudio Fontana & Zorana Grbac & Thorsten Schmidt, 2022. "Term structure modelling with overnight rates beyond stochastic continuity," Working Papers hal-03898872, HAL.
    4. Claudio Fontana & Zorana Grbac & Sandrine Gumbel & Thorsten Schmidt, 2018. "Term structure modeling for multiple curves with stochastic discontinuities," Papers 1810.09882, arXiv.org, revised Dec 2019.
    5. Alessio Calvelli, 2022. "No-Arbitrage Pricing, Dynamics and Forward Prices of Collateralized Derivatives," Papers 2208.08746, arXiv.org, revised Mar 2023.

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