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Strong Bubbles And Strict Local Martingales

Author

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  • MARTIN HERDEGEN

    (ETH Zürich, Mathematik, HG J44, Rämistrasse 101, CH–8092 Zürich, Switzerland)

  • MARTIN SCHWEIZER

    (ETH Zürich, Mathematik, HG G51.2, Rämistrasse 101, CH–8092 Zürich, Switzerland3Swiss Finance Institute, Walchestrasse 9, CH–8006 Zürich, Switzerland)

Abstract

In a numéraire-independent framework, we study a financial market with N assets which are all treated in a symmetric way. We define the fundamental value ∗S of an asset S as its super-replication price and say that the market has a strong bubble if ∗S and S deviate from each other. None of these concepts needs any mention of martingales. Our main result then shows that under a weak absence-of-arbitrage assumption (basically NUPBR), a market has a strong bubble if and only if in all numéraire s for which there is an equivalent local martingale measure (ELMM), asset prices are strict local martingales under all possible ELMMs. We show by an example that our bubble concept lies strictly between the existing notions from the literature. We also give an example where asset prices are strict local martingales under one ELMM, but true martingales under another, and we show how our approach can lead naturally to endogenous bubble birth.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:04:n:s0219024916500229
    DOI: 10.1142/S0219024916500229
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    References listed on IDEAS

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    Cited by:

    1. Gianluca Cassese, 2021. "Complete and competitive financial markets in a complex world," Finance and Stochastics, Springer, vol. 25(4), pages 659-688, October.
    2. Johannes Muhle-Karbe & Marcel Nutz, 2018. "A risk-neutral equilibrium leading to uncertain volatility pricing," Finance and Stochastics, Springer, vol. 22(2), pages 281-295, April.
    3. Martin Herdegen & Dorte Kreher, 2021. "Bubbles in discrete time models," Papers 2104.12740, arXiv.org, revised Jul 2022.
    4. Dániel Ágoston Bálint & Martin Schweizer, 2018. "Making No-Arbitrage Discounting-Invariant: A New FTAP Beyond NFLVR and NUPBR," Swiss Finance Institute Research Paper Series 18-23, Swiss Finance Institute, revised Mar 2018.
    5. Francesca Biagini & Thomas Reitsam, 2019. "Asset Price Bubbles in market models with proportional transaction costs," Papers 1911.10149, arXiv.org, revised Dec 2020.
    6. Martin Herdegen & Dörte Kreher, 2022. "Bubbles in discrete-time models," Finance and Stochastics, Springer, vol. 26(4), pages 899-925, October.
    7. Martin HERDEGEN & Martin SCHWEIZER, 2016. "Economically Consistent Valuations and Put-Call Parity," Swiss Finance Institute Research Paper Series 16-02, Swiss Finance Institute.
    8. Martin Herdegen & Martin Schweizer, 2018. "Semi‐efficient valuations and put‐call parity," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1061-1106, October.
    9. Francesca Biagini & Jacopo Mancin, 2016. "Robust Financial Bubbles," Papers 1602.05471, arXiv.org.
    10. Michael Schatz & Didier Sornette, 2017. "Uniform Integrability of a Single Jump Local Martingale with State-Dependent Characteristics," Swiss Finance Institute Research Paper Series 17-21, Swiss Finance Institute.
    11. Thomas Krabichler & Josef Teichmann, 2020. "A constraint-based notion of illiquidity," Papers 2004.12394, arXiv.org.

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