Change-Point Analysis of Asset Price Bubbles with Power-Law Hazard Function

Lynch, Christopher and Mestel, Benjamin (2019). Change-Point Analysis of Asset Price Bubbles with Power-Law Hazard Function. International Journal of Theoretical and Applied Finance, 22(7), article no. 1950033.

DOI: https://doi.org/10.1142/S021902491950033X

Abstract

We present a methodology to identify change-points in financial markets where the governing regime shifts from a constant rate-of-return, i.e. normal growth, to superexponential growth described by a power-law hazard rate. The latter regime corresponds, in our view, to financial bubbles driven by herding behaviour of market participants. Assuming that the time series of log-price returns of a financial index can be modelled by arithmetic Brownian motion, with an additional jump process with power-law hazard function to approximate the superexponential growth, we derive a threshold value of the hazard-function control parameter, allowing us to decide in which regime the market is more likely to be at any given time. An analysis of the Standard \& Poors 500 index over the last 60 years provides evidence that the methodology has merit in identifying when a period of herding behaviour begins, and, perhaps more importantly, when it ends.

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