On Rational Bubbles and Fat Tails

On Rational Bubbles and Fat Tails*

This paper addresses the statistical properties of time series driven by rational bubbles à la Blanchard and Watson (1982). Using insights on the behavior of multiplicative stochastic processes, we demonstrate that the tails of the unconditional distribution emerging from such bubble processes follow power-laws (exhibit hyperbolic decline). More precisely, we find that rational bubbles predict ...

Multi-dimensional Rational Bubbles and Fat Tails *

We extend the model of rational bubbles of [Blanchard, 1979] and [Blanchard and Watson, 1982] to arbitrary dimensions d: a number d of market time series are made linearly interdependent via d × d stochastic coupling coefficients. We first show that the no-arbitrage condition imposes that the non-diagonal impacts of any asset i on any other asset j = i has to vanish on average, i.e., must exhib...

Rational and Irrational Bubbles

Fat Tails

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Endogenous Rational Bubbles

A weighted replicator dynamic describes how agents switch between a forecast based on fundamentals, a rational bubble forecast and a re‡ective forecast, a weighted average of the former two. If the innovations to the extraneous martingale have a similar magnitude to those of the dividend process and agents are su¢ ciently aggressive in switching forecasting strategies, a signi…cant portion of t...