Stochastic modelling for financial bubbles and policy

Abstract

In this paper, we draw upon the close relationship between statistical physics and mathematical finance to develop a suite of models for financial bubbles and crashes. By modifying previous approaches, we are able to derive novel analytical formulae for evaluation problems and for the expected timing of future change points. In particular, we help to explain why previous approaches have systematically overstated the timing of changes in market regime. The list of potential empirical applications is deep and wide ranging, and includes contemporary housing bubbles, the Eurozone crisis and the Crash of 2008.

Keywords:

• econophysics
• bubbles
• crashes
• expected crash-time

Public Interest Statement

By drawing upon close links between statistical physics and mathematical finance, we provide a mathematical description of bubbles and crashes. From an academic perspective by refining previous approaches, we are able to make a contribution to the underlying theory. However, this research provides support to both policy-makers and academicians. This is reinforced by the list of potential applications which includes housing bubbles, the Eurozone crisis and the Crash of 2008.

Notes

1 In the sequel we note that the case of an anti-bubble is the same basic model but with $v$ replaced by $-v$ throughout Yan, Woodard, and Sornette (2012).

Additional information

Funding

The author has received no direct funding for this research.

Notes on contributors

John Fry

John Fry has a PhD in Probability and Statistics, and an MSc in Statistics and a BSc in Mathematics and Statistics from the University of Newcastle-upon-Tyne. His research interests are in mathematical finance, econophysics, and operational research. He is a member of the Centre for Research into Accounting and Finance in Context (CRAFiC) at Sheffield University Management School.