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Chaos and Bifurcation in 2007-08 Financial Crisis — December 12, 2009

The impact of increasing leverage in the economy produces hyperreaction of market participants to variations of their revenues. If the income of banks decreases, they mass-reduce their lendings; if corporations sales drop, and due to existing debt they cannot adjust their liquidities by further borrowings, then they must immediately reduce their expenses, lay off staff, and cancel investments. This hyperreaction produces a bifurcation mechanism, and eventually a strong dynamical instability in capital markets, commonly called systemic risk. In this article, we show that this instability can be monitored by measuring the highest eigenvalue of a matrix of elasticities. These elasticities measure the reaction of each sector of the economy to a drop in its revenues from another sector. This highest eigenvalue - also called the spectral radius - of the elasticity matrix, can be used as an early indicator of market instability and potential crisis. Grandmont [85] and subsequent research showed the possibility that the "invisible hand" of markets become chaotic, opening the door to uncontrolled swings. Our contribution is to provide an actual way of measuring how close to chaos the market is. Estimating elasticities and actually generating the indicators of instability will be the topic of forthcoming research.
Authors: Youngna Choi, Raphael Douady
papers.ssrn.com
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Topics in Market Micro-Structure

Amsterdam University Press published doctoral thesis of Riskdata's researcher Ilija Zovko. The title of Dr. Zovko's thesis is "Topics in Market Micro-Structure". The thesis was defended in 2008 and advised by Professor Doyne Farmer of Santa Fe Institute in New Mexico, a world foremost authority in market micro-structure, and Professor Cars Homes, of Amsterdam University, well known for his research in non-linear market dynamics.
Authors: Ilija Zovko
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On Probability Characteristics of "Downfalls" in a Standard Brownian Motion, Theory of Probability and Applications, vol. 44, no1, 2000.

Authors: Raphael Douady, Albert Shiryaev and Marc Yor, Riskdata
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Static Hedging of Barrier Options with a Smile: An Inverse Problem, C.O.C.V., 2001

Authors: Claude Bardos, Raphael Douady and Andrei Fursikov, Riskdata
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“This is a challenging and exciting time. Risk managers and senior executives should be seeking more from risk management. Their role needs to evolve as financial institutions increasingly recognize the opportunities and value of a better understanding of risk.”

Phil Rivett
PricewaterhouseCoopers UK