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Economics-Based Financial Bubbles (and Why They Imply Strict Local Martingales)

Author

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  • Martin HERDEGEN

    (ETH Zurich)

  • Martin SCHWEIZER

    (ETH Zurich and Swiss Finance Institute)

Abstract

We introduce a new and numéraire-independent approach for defining and analysing financial bubbles in general, incomplete markets. We define our concepts in an economically motivated way using only primal quantities like assets and trading strategies. We then derive dual characterisations involving numéraires and martingale measures and show that a market is (interesting) bubbly in our sense if and only if all possible valuation measures for all possible discounted asset prices always lead to strict local martingales. In contrast to other approaches for bubble definitions in incomplete markets, our notion of a bubble is robust in the sense that it does not depend on the choice of a particular risk-neutral measure. We illustrate our results and concepts by many explicit and concrete examples; these include an incomplete market which is (interesting) bubbly, an incomplete market where one valuation measure sees a bubble while a second does not, and a natural setup where bubble birth occurs endogenously.

Suggested Citation

  • 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.
    • Handle: RePEc:chf:rpseri:rp1505
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    References listed on IDEAS

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    Cited by:

    1. Travis Fisher & Sergio Pulido & Johannes Ruf, 2017. "Financial Models with Defaultable Numéraires," Working Papers hal-01240736, HAL.
    2. Travis Fisher & Sergio Pulido & Johannes Ruf, 2015. "Financial Models with Defaultable Num\'eraires," Papers 1511.04314, arXiv.org, revised Oct 2017.

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    More about this item

    Keywords

    bubble; incomplete financial market; fundamental value; strict local martingale; numéraire; viability; efficiency; no dominance;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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