Calculation of Probability Distribution of Future Stock Price Indices Based on Geometric Brownian Model

Forecasting is an essential and growing component of financial theories and applications. Forecasts are expressed in three ways: point, interval, and probability distribution. The largest amount of information a forecast can provide is in the form of a probability distribution. For example, in addition to the mean and conditional variance of other torques including kurtosis and skewness, the probability distribution can also be calculated. This form of forecasting is very important in the financial economy, which is a fundamental risk assessment and uncertainty. Because the sum of all possible events is estimated and the future events may not be missed. Therefore, estimating uncertainty in this case is much more accurate than other forms of forecasting. In the present study, based on the Geometric Brownian Model (GBM), the probability of future stock price index values of Tehran Stock Exchange is calculated. Bayesian parametric approach and MCMC sampling algorithm are used for this purpose. The results show the growth rate of the stock price index at an average rate of 4% in the year 1398 (forecast year) and the probability of limiting events such as the index falling to below the 1397 average is very low (about 7%). The results also show that the probability of falling stock price index in the forecast year is lower than the minimum of the previous year is only 0.0017. Therefore, investing in the stock market is very safe. This information is only available in the manner of predicting the probability of future stock price indexes.