Author(s)

Shuaiqi Zhou ¹

Affiliation(s)

¹ Tianjin Yinghua Experimental School, Tianjin, China

Corresponding Author

Shuaiqi Zhou

ABSTRACT

The purpose of this research is to investigate the utilization of the Brownian model in the analysis of financial data. In the field of finance, the analysis of financial data is crucial for making investment decisions and managing risks. The classical stochastic process model, known as the Brownian model, has been extensively employed in this domain. This paper provides an overview of the Brownian model, discusses its advantages and limitations in analyzing financial data, and presents empirical research findings. These findings serve as valuable references for future studies. The primary focus of the Brownian model is to study the random fluctuations of a variable while adhering to a specific statistical pattern. In this study, we derive the Brownian equation and explore the meanings of the damping term and the random variable term within the equation. When the random variable exhibits complete randomness at different time points, it is referred to as white noise. However, when considering certain time correlation lengths, the solution to the Brownian equation becomes more intricate. We meticulously examine how different noise terms and damping terms influence the solutions of the equation. Furthermore, we establish connections between these variables and various financial variables, particularly stock prices, to gain a practical understanding of the Brownian equation. The evolution of stock prices under different parameters is graphically illustrated and analyzed in detail.

KEYWORDS

Brownian equation, stochastic evolution, partial differential equation, random variables, stock price

CITE THIS PAPER

Shuaiqi Zhou, The Stochastic Model of Stock Prices. Accounting, Auditing and Finance (2023) Vol. 4: 48-53. DOI: http://dx.doi.org/10.23977/accaf.2023.040207.

REFERENCES

[1] Zigang Huang, Yong Chen, Yong Zhang, Yinghai Wang. (2007) Description of dynamics of stock prices by a Langevin approach. Chinese Physics, 16, 1009.
[2] Jean-Philippe Bouchaud, Rama Cont. (1998) A Langevin Approach to Stock Market Fluctuations and Crashes. The European Physical Journal, B 6(4):543-550.
[3] J. P. Singh. Stock Market Modeling in the Langevin Formalism. International Journal of Financial Management, 8 (4) 2018, 01-06, http://publishingindia.com/ijfm/ 
[4] Bernd Rosenow, Fluctuations and Market Friction in Financial Trading. International Journal of Modern Physics C, Vol. 13, No. 3 (2002) 1–7
[5] M. Jannesar, A. Sadeghi, E. Meyer, G. R. Jafari. (2019) A Langevin equation that governs the irregular stick-slip nano-scale friction. Scientific Reports volume 9, Article number: 12505.

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