Inefficient Bubbles and Efficient Drawdowns in Financial Markets

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 crisis. 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. Our framework also allows us to elucidate the status of rational expectation bubbles, which are by design afflicted with an inherent error in both discrete and continuous time models that can be traced down to a problematic definition of the fundamental value. While the discrete time case has been extensively discussed in the literature and is most criticized for a structure that is based on a payoff at infinity, we show that a new version of this error also permeates the continuous, finite time “strict local martingale”-approach to bubbles. In summary, our framework will simplify and foster interdisciplinary exchange at the intersection of economics and mathematical finance and encourage further research.