Probability and statistics are widely applied in the modern financial market, and it contributes and prompts the study in stock market analysis. The Brownian motion particularly plays a key role in the scenario on the prediction of stock volatility. This paper is going to discuss the fundamental mathematical and statistical theories applied in the simulation of stock volatility. It involves the introduction to geometric Brownian motion, stochastic process, random walk, and some important statistical theorems. The most frequent model for modeling stock prices is Geometric Brownian Motion (GBM). GBM posits that random shocks accompany a continuous drift. While period returns are normally distributed under GBM, multiperiod price levels (for example, ten days) are lognormally distributed. Forecasting of stock prices acts as an important challenge in nowadays stock market decision.
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