On Crises in Financial Markets


  • Vladimir A. Popov Financial University under the Government of the Russian Federation, Moscow




Financial markets, asset prices, price emissions, risks, the quantum nature of information, resonance phenomena, density wave function, quantum oscillator.


The reasons of the financial markets collapse and methods of their forecasting are investigated in this article. A model based on hypothesis of the quantum nature of the impact of information on financial markets is given. It is shown that in information-saturated volatile financial markets, sharp price jumps are really expected

Motivation for this research is inability of traditional approach for explaining sharp price jumps during financial crises. They are unexpected according to the traditional theories. When considering the logarithm of relative price changes over the period ytk = ln(Ntk/Ntk-1) it was found that the statistical characteristics of this random value differ from the characteristics of the normal distribution. The approach, developed in this paper, explaining the possibility of sharp price jumps, seems to be more harmonious than the traditional approach.

Novelty of given approach consists in considering a model based on the assumption about the quantum (discontinuous) nature of information impact on financial markets. The process of information transfer is quantum – i. e. the information is transmitted in portions, multiples of a quantum of information. There are discrete information levels. When moving from one level to another, it is necessary to absorb or emit one quantum of information. Thus, the amount of information of a particular level is necessarily a multiple of the quantum of information.

Methodology and methods are based on probability and differential equations. Equation with respect to logarithm of increment of prices y = ln(N(t0+Dt)/N(t0)) is thoroughly investigated. The probability density function for each information price level Pn(y) = Y2n(y), where Y(y) is called the wave function of prices. Equation with respect to Y(y) is thoroughly investigated too.

There are many calculations of various probabilities and other characteristics of y (logarithm of prices increment) for different information price level. The hierarchy of information-price levels is autonomous – i.e. each of them has its own separate probability characteristics, different functions of probability density distribution. The normal distribution takes place only when n=0. For all others n=1, 2, 3... the density functions are different from Gaussian.


Brusov P., Filatova T., Orekhova N., Kulik V., Wail I., Brailov A. The impact of the central bank key rate and commercial banks credit rates on creating and maintaining of a favorable climate in the country // Journal of Reviews on Global Economics 7: 360-376.
Fama E.F. The behavior of stock market prices // Journal of Business. V. 34. P.420-429, 1965.
Guillaume D.M., Dacorona M.M., Dave R.R., Muller V.A., Olsen R.B., Pictet O.V. From the bird’s eye to the microscope: A survey of new stylized facts of the intra-daily foreign exchange markets // Finance and Stochastic. V.1. ? 2 P. 95-129, 1997.
Landau L.D., Lifshitz E.M. Quantum Mechanics. Non Relativistic Theory. Pergamon Press Ltd. 1977.
Mandelbroot B.B. Some noises with 1/f spectrum: a bridge between direct currant and white noise // IEEE Transactions of Information Theory. April, 1967.
Mandelbroot B.B. Robustness of the rescaled range R/S in the measurement of noncyclic long-run statistical dependence // Water Resources Research. V.5, ? 5. P. 967-988, 1969.
Mandelbroot B.B. Statistical methodology for non-periodic cycles: from the covariance to R/S analysis // Annals of Economic and Social Measurement. V.1., ?3. P. 259-290, 1972.
Mantegna R.N., Stanley H.E. Scaling behavior in the dynamics of an economic index // Nature. V. 376. P. 46-49, 1995
Popov V.A. Inflation and consumer basket // Journal of Reviews on Global Economics 7: 453-456.
Samuelson P.A. Proof that property anticipated prices fluctuate randomly // Industrial Management Review. V.6. P. 41-49, 1965