INEFFICIENT BUBBLES AND EFFICIENT DRAWDOWNS IN FINANCIAL MARKETS

Michael Schatz and Didier Sornette
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Michael Schatz: Department of Management, Technology and Economics, ETH Zurich, Scheuchzerstrasse 7, Zurich 8092, Switzerland
Didier Sornette: Department of Management, Technology and Economics, ETH Zurich, Zurich, Switzerland3Swiss Finance Institute, c/o University of Geneva, Geneva, Switzerland4Institute of Risk Analysis, Prediction and Management (Risks-X), Academy for Advanced Interdisciplinary Studies, SUSTech, Shenzhen, P. R. China

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 07, 1-56

Abstract: At odds with the common “rational expectations” framework for bubbles, economists like Hyman Minsky, Charles Kindleberger and Robert Shiller have documented that irrational behavior, ambiguous information or certain limits to arbitrage are essential drivers for bubble phenomena and financial crises. Following this understanding that asset price bubbles are generated by market failures, we present a framework for explosive semimartingales that is based on the antagonistic combination of (i) an excessive, unstable pre-crash process and (ii) a drawdown starting at some random time. This unifying framework allows one to accommodate and compare many discrete and continuous time bubble models in the literature that feature such market inefficiencies. Moreover, it significantly extends the range of feasible asset price processes during times of financial speculation and frenzy and provides a strong theoretical background for future model design in financial and risk management problem settings. This conception of bubbles also allows us to elucidate the status of rational expectation bubbles, which, by design, suffer from the paradox that a rational market should not allow for misvaluation. While the discrete time case has been extensively discussed in the literature and is most criticized for its failure to comply with rational expectations equilibria, we argue that this carries over to the finite time “strict local martingale”-approach to bubbles.

Keywords: Financial bubbles; financial crashes; explosive processes; bubble decomposition; strict local martingale approach; infinite horizon bubbles (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219024920500478

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