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Fragility of arbitrage and bubbles in local martingale diffusion models

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  • Paolo Guasoni
  • Miklós Rásonyi

Abstract

For any positive diffusion with minimal regularity, there exists a semimartingale with uniformly close paths that is a martingale under an equivalent probability. As a result, in models of asset prices based on such diffusions, arbitrage and bubbles alike disappear under proportional transaction costs or under small model mis-specifications. Thus, local martingale diffusion models of arbitrage and bubbles are not robust to small trading and monitoring frictions. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Paolo Guasoni & Miklós Rásonyi, 2015. "Fragility of arbitrage and bubbles in local martingale diffusion models," Finance and Stochastics, Springer, vol. 19(2), pages 215-231, April.
    • Handle: RePEc:spr:finsto:v:19:y:2015:i:2:p:215-231
    DOI: 10.1007/s00780-015-0256-0
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    References listed on IDEAS

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    Cited by:

    1. Mikl'os R'asonyi & Hasanjan Sayit, 2015. "Sticky processes, local and true martingales," Papers 1509.08280, arXiv.org, revised Mar 2017.
    2. Martin Herdegen, 2017. "No-Arbitrage In A Numéraire-Independent Modeling Framework," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 568-603, April.
    3. Christoph Czichowsky & Walter Schachermayer, 2015. "Portfolio optimisation beyond semimartingales: shadow prices and fractional Brownian motion," Papers 1505.02416, arXiv.org, revised Aug 2016.
    4. Antoine Jacquier & Martin Keller-Ressel, 2015. "Implied volatility in strict local martingale models," Papers 1508.04351, arXiv.org.
    5. José Carlos Dias & João Pedro Vidal Nunes & Aricson Cruz, 2020. "A note on options and bubbles under the CEV model: implications for pricing and hedging," Review of Derivatives Research, Springer, vol. 23(3), pages 249-272, October.
    6. Bal'azs Gerencs'er & Mikl'os R'asonyi, 2020. "Invariant measures for multidimensional fractional stochastic volatility models," Papers 2002.04832, arXiv.org, revised Aug 2021.
    7. Martin HERDEGEN & Martin SCHWEIZER, 2015. "Economics-Based Financial Bubbles (and Why They Imply Strict Local Martingales)," Swiss Finance Institute Research Paper Series 15-05, Swiss Finance Institute.
    8. Francesca Biagini & Thomas Reitsam, 2019. "Asset Price Bubbles in market models with proportional transaction costs," Papers 1911.10149, arXiv.org, revised Dec 2020.
    9. Martin Herdegen & Martin Schweizer, 2016. "Strong Bubbles And Strict Local Martingales," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-44, June.
    10. Herdegen, Martin & Herrmann, Sebastian, 2016. "Single jump processes and strict local martingales," Stochastic Processes and their Applications, Elsevier, vol. 126(2), pages 337-359.
    11. Eckhard Platen & Stefan Tappe, 2020. "Exploiting arbitrage requires short selling," Papers 2011.12523, arXiv.org, revised Sep 2022.

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    More about this item

    Keywords

    Arbitrage; Bubbles; Transaction costs; Local martingales; 91G10; 62P05; G12;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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