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Asset Price Bubbles in Complete Markets

Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Summary

This paper reviews and extends the mathematical finance literature on bubbles in complete markets. We provide a new characterization theorem for bubbles under the standard no-arbitrage framework, showing that bubbles can be of three types. Type 1 bubbles are uniformly integrable martingales, and these can exist with an infinite lifetime. Type 2 bubbles are nonuniformly integrable martingales, and these can exist for a finite, but unbounded, lifetime. Last, Type 3 bubbles are strict local martingales, and these can exist for a finite lifetime only. When one adds a no-dominance assumption (from Merton [24]), only Type 1 bubbles remain. In addition, under Merton’s no-dominance hypothesis, put–call parity holds and there are no bubbles in standard call and put options. Our analysis implies that if one believes asset price bubbles exist and are an important economic phenomena, then asset markets must be incomplete.

Key words

Bubbles no free lunch with vanishing risk (NFLVR) complete markets local martingale put–call parity derivative pricing 

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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  1. 1.Johnson Graduate School of ManagementCornell UniversityIthacaUSA
  2. 2.School of Operations Research and Industrial EngineeringCollege of Engineering Cornell UniversityIthacaUSA

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