Applying the mathematical apparatus of fluid and gas dynamics for financial market dynamics modeling

A.R. Musin^a∗, A.S. Sorokin^b,c∗∗

^aVTB Bank, Moscow, 123100 Russia

^bPlekhanov Russian University of Economics, Moscow, 117997 Russia

^cMoscow University of Finance and Industry “Synergy”, Moscow, 125190 Russia

E-mail: ^∗amusin@nes.ru, ^∗∗alsorokin@mail.ru

Received May 16, 2018

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Abstract

This paper is devoted to the study of possibilities for using the mathematical apparatus of natural science research, in particular the parabolic type differential equations and stochastic modeling methods in order to explain the behavioral features of financial market. An econometric model has been presented that explains the market prices dynamics based on Burger’s differential equation, which is used for modeling liquids and gas motion. The model’s structure allows to account for traditional dynamic features of financial market that is, in particular, related to traders behavioral patterns, as well as such price effects associated with the presence of local linear trend. Model testing has been performed on minute market data of pound sterling to US dollar exchange rate for the whole 2017 year and confirmed the possibility of using it for predicting the considered currency pair values with the accuracy of 57.2% measured by the percentage of correct forecast direction, while the value of the corresponding indicator for a random walk model, additionally reviewed for comparison purposes, was only 49.8%.

Keywords: financial market, forecasting, econometric models, Kalman filter

References

1. Pearson K. Problem of the random walk. Nature, 1905, vol. 72, no. 1865, pp. 294–301. doi: 10.1038/072294b0.
2. Kemp A.G., Reid G.C. The random walk hypothesis and the recent behaviour of equity prices in Britain. Economica, 1971, vol. 38, no. 149, pp. 28–51. doi: 10.2307/2551749.
3. Newbold P., Rayner T., Kellard N., Ennew C. Is the dollar/ECU exchange rate a random walk? Appl. Financ. Econ., 1998, vol. 8, no. 6, pp. 553–558. doi: 10.1080/096031098332583.
4. Yura Y., Takayasu H., Sornette D., Takayasu M. Financial Brownian particle in the layered order-book fluid and fluctuation-dissipation relations. Phys. Rev. Lett., 2014, vol. 112, no. 9, art. 098703 , pp. 1–5. doi: 10.1103/PhysRevLett.112.098703.
5. Ghashghaie S., Breymann W., Peinke J., Talkner P., Dodge Y. Turbulent cascades in foreign exchange markets. Nature, 1996, vol. 381, pp. 767–770. doi: 10.1038/381767a0.
6. Mantegna R.N., Stanley H.E. Turbulence and financial markets. Nature, 1996, vol. 383, pp. 587–588. doi: 10.1038/383587a0.
7. Kac M. Random walk and the theory of Brownian motion. Am. Math. Mon., 1947, vol. 54, no. 7, pt. 1, pp. 369–391. doi: 10.2307/2304386.
8. Lord Rayleigh F.R.S. On the resultant of a large number of vibrations of the same pitch and of arbitrary phase. Philos. Mag. J. Sci., 1880, vol. 10, no. 60, pp. 73–78.
9. Malkiel B.G. The efficient market hypothesis and its critics. J. Econ. Perspect., 2003, vol. 17, no. 1, pp. 59–82. doi: 10.1257/089533003321164958.
10. Black F., Scholes M. The pricing of options and corporate liabilities. J. Polit. Econ., 1973, vol. 81, no. 3, pp. 637–654.
11. Jablonska M., Kauranne T. Multi-agent stochastic simulation for the electricity spot market price. In: Osinga S., Hofstede G., Verwaart T. (Eds.) Emergent Results of Artificial Economics. Lecture Notes in Economics and Mathematical Systems. Vol. 652. Berlin, Heidelberg, Springer, 2011, pp. 3–14. doi: 10.1007/978-3-642-21108-9 1.
12. Weinan E., Khanin K., Mazel A., Sinai Ya. Invariant measures for Burgers equation with stochastic forcing. Anna. Math., 2000, vol. 151, no. 3, pp. 877–960. doi: 10.2307/121126.
13. Bianchi A., Capasso V., Morale D. Estimation and prediction of a nonlinear model for price herding. In: Complex Models and Intensive Computational Methods for Estimation and Prediction. Padova, CLUEP, 2005, pp. 365–370.
14. Cheung Y.-W., Chinn M.D. Currency traders and exchange rate dynamics: A survey of the US market. J. Int. Money Finance, 2001, vol. 20, no. 4, pp. 439–471. doi: 10.1016/S0261-5606(01)00002-X.
15. Taylor M., Allen H. The use of technical analysis in the foreign exchange market. J. Int. Money Finance, 1992, vol. 11, no. 3, pp. 304–314. doi: 10.1016/0261-5606(92)90048-3.
16. Durbin J., Koopman S.J. A simple and efficient simulation smoother for state space time series analysis. Biometrika, 2002, vol. 89, no. 3, pp. 603–615.
17. Musin A.R. Economic-mathematical model for predicting financial market dynamics. Stat. Ekon., 2018, vol. 15, no. 4, pp. 61–69. (In Russian)
18. Kalman R.E., Bucy R.S. New results in linear filtering and prediction theory. J. Basic Eng., 1961, vol. 83, no. 1, pp. 95–108. doi: 10.1115/1.3658902.
19. Musin A.R. Efficiency comparison of FX market’s forecasting models with Kalman’s filtering and traditional time series models. Naukovedenie, 2017, vol. 9, no. 3, pp. 37–47. (In Russian)
20. Tsypin A.P., Sorokin A.S. Statistical software packages in social and economic researchers. Azimut Nauchn. Issled.: Ekon. Upr., 2016, vol. 5, no. 4, pp. 379–384. (In Russian)

For citation: Musin A.R., Sorokin A.S. Applying the mathematical apparatus of fluid and gas dynamics for financial market dynamics modeling. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 4, pp. 709–717. (In Russian)

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