Finite-time singularities in the dynamics of Mexican financial crises

Historically, symptoms of Mexican financial crises have been strongly reflected in the dynamics of the Mexican peso to the dollar exchange currency market. Specifically, in the Mexican financial crises during 1990's, the peso suffered significant depreciation processes, which has important impacts in the macro- and micro-economical environment. In this paper, it is shown that the peso depreciation growth was greater than an exponential and that these growth rates are compatible with a spontaneous singularity occurring at a critical time, which signals an abrupt transition to new dynamical conditions. As in the major 1990's financial crisis in 1994–1995, some control actions (e.g., increasing the USA dollar supply) are commonly taken to decelerate the degree of abruptness of peso depreciation. Implications of these control actions on the crisis dynamics are discussed. Interestingly, by means of a simple model, it is demonstrated that the time at which the control actions begin to apply is critical to moderate the adverse effects of the financial crisis.