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Geometric Brownian Motion & Nifty 50 Index: A Confirmation from National Stock Exchange

Author Details ( * ) denotes Corresponding author

1. * Amit Kundu, Associate Professor, Department of Commerce, Cooch Behar Panchanan Barma University, Cooch Behar, West Bengal, India (

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.
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.


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

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