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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