Predicting Financial Market Crashes Using Ghost Singularities

Damian Smug,Didier Sornette,Peter Ashwin

doi:10.2139/ssrn.2990488

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.

Highlights

Forecasting market behaviour has been a topic of general interest for hundreds of years
There are models exploring the impact of the dynamics between traders, other models attempt to capture the effects of feedbacks between financial information and investment strategies using various stochastic non-linear processes
These references can be conceptually linked to the pioneering work of [11,12,13,14,15,16] describing the dynamical behaviour of heterogeneous markets with many trader types using dynamical system concepts, including limit cycles as the large type limit of interaction agents, bifurcation routes to instability and strange attractors in evolutionary financial market models

Summary

Introduction

Forecasting market behaviour has been a topic of general interest for hundreds of years. [7,8,9,10]) These references can be conceptually linked to the pioneering work of [11,12,13,14,15,16] describing the dynamical behaviour of heterogeneous markets with many trader types using dynamical system concepts, including limit cycles as the large type limit of interaction agents, bifurcation routes to instability and strange attractors in evolutionary financial market models. This variety suggests that the concepts and methods of complex dynamical systems could be useful in the area of financial markets.

Objectives

Findings

Conclusion