Financial crisis dynamics: Attempt to define a market instability indicator

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 they cannot adjust their liquidities by further borrowing due to existing debt, 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 that is 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-the spectral radius-of the elasticity matrix can be used as an early indicator of market instability and potential crisis. Grandmont and subsequent research showed the possibility that the 'invisible hand' of markets becomes 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.