Alexander Smirnov1
  • 1 National Research University Higher School of Economics, 20 Myasnitskaya Str., Moscow, 101000, Russian Federation

Logistic Model of Financial Leverage

2013. Vol. 17. No. 4. P. 617–648 [issue contents]
The model of financial leverage dynamics that had been proposed by the author (the journal of «Voprosy Economiki», 2012) was investigated and developed further. Aggregate structure of a financial system was introduced via spreads between different asset returns while its behavior was represented by the leverage. Logistic model proved to be convenient in formalization of the Wicksellian analysis of a credit market. Being applied to the study of collective investors’ behavior near a stationary leverage, the model showed that the normal credit market had a stable stationary point, called a «Wicksellian equilibrium». In its local neighborhood different investment strategies did not give rise to the credit expansion. Contrary to that, a conjugate stationary point, corresponding to the irrational market, appeared to be an unstable one. In its neighborhood the market behavior could be decomposed into two branches that should be analyzed separately. Along so called «Minsky branch» a financial bubble being fuelled by the credit expansion has been formed, evolved and ultimately burst, suggesting the system’s singularity. Another, the «Fisher branch», near the unstable point has demonstrated the process of deleveraging that drove the system toward its collapse but under different economic conditions. Interestingly, that trajectory might have included some unstable states having the symptoms of the improved market conditions. Thus, the metastable qualities of a financial system, though harmful and highly undesirable, are by no means «paradoxical», contrary to the well known Verhulst model of a biological population. Using the IMF information the model predicted family of the leverage trajectories for the global financial system.

Citation: (2013) Logisticheskaya model': determinirovannaya dinamika finansovogo rychaga [Logistic Model of Financial Leverage]. HSE Economic Journal, 4, pp. 617-648 (in Russian)
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