Subject. The article addresses the stable functioning of the financial market and its protection against financial crises as the main indicator of financial system’s stability. It considers the history of the issue, enabling to conclude that financial markets are built mainly on the principle of unstable equilibrium in contrast to the more stable equilibrium underlying the commodity markets and industrial production. Objectives. The article attempts to compare well-known stochastic models with dynamic and chaotic systems. Methods. The study employs stochastic modeling (autoregressive conditional heteroscedasticity (ARCH) and generalized autoregressive conditional heteroscedasticity (GARCH) models), investigates methods and approaches to solving some types of differential stochastic equations, in particular, the Ito and Fokker-Planck-Kolmogorov equations. Results. Financial markets are considered within the theory of dynamic systems as an example of a non-linear system. It is extremely difficult to predict the behavior of such a system, precisely because of the non-linearity, which is reduced to random and chaotic processes. Through mathematical transformations, the paper shows that solutions are reduced to multidimensional stochastic volatility models. Conclusions. Stochastic volatility models, despite their relative theoretical elaboration and practical applicability, can lead to dynamic chaos, when there is a vector of asset return, the conditional covariance matrix of which changes over time.
Il'yasov S.M. [The nature and major factors of the banking system’s stability]. Den'gi i kredit = Russian Journal of Money and Finance, 2006, no. 2, pp. 45–48. (In Russ.)
Lakshina O.A., Chekmareva E.N. [Analysis and assessment of financial system stability]. Den'gi i kredit = Russian Journal of Money and Finance, 2005, no. 10, pp. 24–29. (In Russ.)
Kydland F.E., Prescott E.C. Time to Build an Aggregate Fluctuations. Econometrica, 1982, vol. 50, no. 6, pp. 1345–1370. URL: Link
Kondrat'ev N.D. Problemy ekonomicheskoi dinamiki [Problems of economic dynamics]. Moscow, Ekonomika Publ., 1989, 523 p.
Dou Sh. [The psychology of financial markets: Keynes, Minsky and emotional finance]. Voprosy Ekonomiki, 2010, no. 1, pp. 99–113. (In Russ.) URL: Link
Minsky H.P. The Financial Instability Hypothesis: An Interpretation of Keynes and an Alternative to “Standard” Theory. Nebraska Journal of Economics and Business, 1977, vol. 16, no. 1, pp. 5–16. URL: Link
Skorobogatov A. [Stock market, the institutional structure and stability problem in the capitalist economy]. Voprosy Ekonomiki, 2006, no. 12, pp. 80–97. (In Russ.) URL: Link
Kindleberger C.P., Aliber R. Manias, Panics, and Crashes: A History of Financial Crises. Hoboken, NJ, John Wiley & Sons, 2005, 5th edition, 355 p.
Mishkin F. Ekonomicheskaya teoriya deneg, bankovskogo dela i finansovykh rynkov [The economic theory of money, banking and financial markets]. Moscow, Aspekt Press Publ., 1999, 820 p.
Shiryaev A.N. Osnovy stokhasticheskoi finansovoi matematiki. T. 1. Fakty, modeli [Fundamentals of stochastic financial mathematics. Vol. 1. Facts, models]. Moscow, FAZIS Publ., 1998, 512 p.
Campbell J.Y., Lo A.W., MacKinlay A.C. The Econometrics of Financial Markets. Princeton, Princeton University Press, 1996, 632 p.
Engle R.F. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 1982, vol. 50, no. 4, pp. 987–1007. URL: Link
Bollerslev T. Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics, 1986, vol. 31, pp. 307–327. URL: Link