Journal Press India^®

Author Details ( * ) denotes Corresponding author

Purpose: The study's major goal is to create a model for projecting the Nifty 50 closed stock price's short-term return distribution. 
Design/Methodology/Approach: A stochastic process, has been followed in the current study. Geometric Brownian Motion has been used for managing investment risk.  The article has used Geometric Brownian Motion for managing investment risk.  Nifty 50 closed prices have been used for this study.
Findings: The Kolmogorov-Smirnov (K-S) statistic of Nifty 50 closed stock price for 226 days from the 13th July, 2020 to the 9th June, 2021 is 0.253113. As calculated K-S stat 0.253113 is less than table value 1.35810, the series is normally distributed. The Q-Q plot shows that with the dots forming a fairly straight line and the data set is normal distribution. The goal of the selection procedure between all simulations is to guarantee that the forecast data in the return distribution have the same structure and trend as the Nifty 50 closing stock price. 
Research Limitations/Implications: It considers the data from the 13th July, 2020 to the 9th June, 2021 is used in this article to determine whether the data are normally distributed and viable to estimate for future stock prices.
Practical Implications: The technician's major purpose is to make profit at the expense of other investors.  He should find high volatile stocks in any holding period for effective forecast. Regulatory bodies in the market should focus on long-term stability by accumulating reserves that can cushion off the consequences of illiquidity, especially in the period of significant volatility.
Originality/Value: 
Geometric Brownian Motion model is used to forecast.  It is more accurate model in compare to other models. Investors can take shelter of this model for their investment’s decision. K-S test & Q-Q plot method are used for the normality test.  Simulation is used by using GBM equation. MAPE is designed to decide the forecast accuracy.

Keywords

Geometric brownian motion; K-S test; Q-Q plot; MAPE.

1. A, E. F. F. is. (1995). Random Walks in Stock Market Prices. Financial Analysts Journal, 51(1), 75–80. https://doi.org/10.2469/faj.v51.n1.1861  
2. Agbam, A. S., & Isukul, A. (2020). STOCHASTIC DIFFERENTIAL EQUATION OF GEOMETRIC BROWNIAN MOTION AND ITS APPLICATION IN FORECASTING OF. Probability Statistics and Econometric Journal, 2(6). 
3. Alhagyan, M., Misiran, M., & Omar, Z. (2017). Surveying the best volatility measurements to forecast stock market. Applied Mathematical Sciences, 11(23), 1113–1122. https://doi.org/10.12988/ams.2017.7397 
4. Bowerman, B. L., O’Connell, R. T., & Koehler., A. B. (2005). Forecasting, time series, and regression : an applied approach. In Belmont, CA : Thomson Brooks/Cole, c2005. Belmont, CA : Thomson Brooks/Cole, ©2005. 
5. Calabrese, R., & Zenga, M., (2010). Bank Loan recovery rates: Measuring and nonparametric density estimation. Journal of Banking and Finance, 34(5), pp. 903–911.
6. Farida Agustini, W., Restu Affianti, I., & Putri, E. R. (2018). Stock price prediction using geometric Brownian motion. Journal of Physics: Conference Series, 974(1). https://doi.org/10.1088/1742-6596/974/1/012047
7. Feller, W. (1948). On the Kolmogorov-Smirnov Limit Theorems for Empirical Distributions. Ann. Math. Statist., 19(2), 177–189. https://doi.org/10.1214/aoms/1177730243
8. Kolmogorov, A. N., (1933). Sulla determinazione empirica di una legge di distribuzione. Giornale dell’Istituto Italiano degli Attuari, 4, pp. 1–11.
9. Marathe, R., & Ryan, S. (2005). One the validity of the geometric Brownian motion assumption. The Engineering Economist: A Journal Devoted to the Problems of Capital Investment, 50(2), 159-192.
10. Niederhausen, H., (1981). Sheffer Polynomials for computing exact 
11. Kolmogorov-Smirnov and R ́enyi type distributions. The Annals of Statistics, pp. 923–944
12. Kumar Si, R., & Bishi, B. (2020). Forecasting Short Term Return Distribution of S&P BSE Stock Index Using Geometric Brownian Motion: An Evidence from Bombay Stock Exchange. International Journal of Statistics and Systems, 15(1), 29–45. http://www.ripublication.com  
13. Ladde, G. S., & Wu, L. (2009). Development of modified Geometric Brownian Motion models by using stock price data and basic statistics. Nonlinear Analysis, 71(12), e1203–e1208. https://doi.org/10.1016/j.na.2009.01.151
14. Marathe, R. R., & Ryan, S. M. (2005). On The Validity of The Geometric Brownian Motion Assumption. A Journal Devoted to the Problems of Capital Investment, 50(2), 159–192. https://doi.org/https://doi.org/10.1080/00137910590949904
15. Reddy, K., & Clinton, V. (2016). Simulating Stock Prices Using Geometric Brownian Motion: Evidence from Australian Companies. Australasian Accounting, Business and Finance Journal, 10(3). https://doi.org/http://dx.doi.org/10.14453/aabfj.v10i3.3
16. Sengupta, C. (2004). Financial Modeling Using Excel and VBA. In John Wiley & Sons, Inc. https://download.e-bookshelf.de/download/0000/5842/69/L-G-0000584269-0002384300.pdf
17. Si K R., & Bidyadhara Bishi (2020). Forecasting short term return distribution of S&P BSE stock index using Geometric Brownian motion: An evidence from Bombay stock exchange. International Journal of Statistics and Systems, 15, pp. 29-45. https://doi.org/10.1016/0005-7967(69)90018-7