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Predicting Financial Market Crashes Using Ghost Singularities

21 Pages Posted: 23 Jun 2017  

Damian Smug

University of Exeter

Peter Ashwin

University of Exeter

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute

Date Written: June 1, 2017

Abstract

We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of that system coupled with standard multiplicative noise rationalises the log-periodic power law singularity pattern documented in many historical financial bubbles. The notion of ‘ghosts of finite-time singularities’ is introduced and used to estimate the end of an evolving bubble, using finite-time singularities of an approximate normal form near the bifurcation point. We test the forecasting skill of this method on different stochastic price realisations and compare with Monte Carlo simulations of the full system. Remarkably, the former is significantly more precise and less biased. Moreover, the method of ghosts of singularities is less sensitive to the noise realisation, thus providing more robust forecasts.

Keywords: Financial Markets, State Space Models, Price Forecasting, Simulation, Bifurcation Theory, Finite-Time Singularity

JEL Classification: C02, C18, C32, G01, G17

Suggested Citation

Smug, Damian and Ashwin, Peter and Sornette, Didier, Predicting Financial Market Crashes Using Ghost Singularities (June 1, 2017). Swiss Finance Institute Research Paper No. 17-23. Available at SSRN: https://ssrn.com/abstract=2990488

Damian Smug

University of Exeter ( email )

Northcote House
The Queen's Drive
Exeter, Devon EX4 4QJ
United Kingdom

Peter Ashwin

University of Exeter ( email )

Northcote House
The Queen's Drive
Exeter, Devon EX4 4QJ
United Kingdom

Didier Sornette (Contact Author)

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Swiss Finance Institute ( email )

c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900
Switzerland

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