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

Financial Assets and their Collateral: The Stochastic Model of Leverage

2014. Vol. 18. No. 2. P. 183–215 [issue contents]
The paper continues investigation of the logistic model of financial leverage. Analogies between collaterized loans with margin calls and macrofinancial leverage are studied. The gamma distribution for the global financial leverage was found and its parameters were estimated on the IMF data about development of the world financial system in 2003–2012. The model was applied in order to estimate the amount of global assets that would have been fully collate­rized by the world GDP. In particular, it was found that about 6 per cent of world financial assets in 2012, or approximately $17tn could be defined as toxic ones. Stochastic logistic model that underlies the process did possess some qualities which significantly differs from its deterministic analogue. As appeared, noise was able to transform the stable deterministic model into unstable stochastic system. If existed, the stochastic attractor coincides with the mode of gamma distribution. It was much smaller than its deterministic analogue, though stochastic trajectories might converge towards zero. The Lyapunov exponent while being the standard measure of the stochastic model stability served as a signal of investors’ confidence in the global markets solvency. Correspondingly, a reduction of gamma distribution to the exponential one could be interpreted as a signal of the financial system destabilization. Hence the crisis might emerge either due to credit expansion and excessive borrowing or as an unintentional outcome of investors’ reluctance to refinance their indebtness because of unusually high volatility. The latter was modeled as a system’s behavior along the “Fisher trajectory” accompanied by decreasing value of the equity market. Such processes could have resulted in the increase of leverage (per unit of GDP) whereby undermining the validity and universality of the no-arbitrage mechanism under uncertainty.

Citation: Smirnov A. (2014) Obespechenie aktivov makrofinansovoy sistemy i stokhasticheskaya dinamika rychaga [Financial Assets and their Collateral: The Stochastic Model of Leverage]. HSE Economic Journal, vol. 18, no 2, pp. 183-215 (in Russian)
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