Bayesian Analysis of Bubbles in Asset Prices

Andras Fulop,Jun Yu

doi:10.3390/econometrics5040047

Abstract

We develop a new model where the dynamic structure of the asset price, after the fundamental value is removed, is subject to two different regimes. One regime reflects the normal period where the asset price divided by the dividend is assumed to follow a mean-reverting process around a stochastic long run mean. The second regime reflects the bubble period with explosive behavior. Stochastic switches between two regimes and non-constant probabilities of exit from the bubble regime are both allowed. A Bayesian learning approach is employed to jointly estimate the latent states and the model parameters in real time. An important feature of our Bayesian method is that we are able to deal with parameter uncertainty and at the same time, to learn about the states and the parameters sequentially, allowing for real time model analysis. This feature is particularly useful for market surveillance. Analysis using simulated data reveals that our method has good power properties for detecting bubbles. Empirical analysis using price-dividend ratios of S&P500 highlights the advantages of our method.

Highlights

The recent global financial crisis and the European debt crisis have prompted economists and regulators to work arduously to find ways to avoid the crisis
We propose a new regime switching model with two regimes, a normal regime and a bubble regime
To estimate the model we use a sequential Bayesian simulation method that allows for real time detection of bubble origination and conclusion

Summary

Introduction

The recent global financial crisis and the European debt crisis have prompted economists and regulators to work arduously to find ways to avoid the crisis. From a historical perspective, Ahamed (2009) argues that financial crises are often preceded by an asset market bubble.. Well-known bubble episodes include the Dutch tulip mania in the 17th century, the British South Sea bubble at the beginning of the 18th century, the Railway mania in the 1840s, the Roaring Twenties stock-market bubble, the Dot-com bubble at the end of the 1990s, and the US housing bubbles lasting until 2006. Bubbles are generally considered harmful to economies and the welfare of society and are thought to lead to the misallocation of resources. Caballero et al (2008) argues that the burst of an asset price bubble can lead to recession in the real economy. Approaches have been tried to detect the presence and the burst of financial bubbles and to estimate the bubble origination and collapsing dates

Methods

Results

Conclusion