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Abstract:
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Geometric Brownian motion (GBM) model basically suggests that the distribution of asset returns is normal or lognormal. But, many empirical studies have revealed that return distributions are usually not normal. These studies time and again discover evidence of non-normality, such as heavy tails, excess kurtosis, etc. This paper recommends the GBM model based upon the t-distribution to approximate the return distributions of assets, and compares the distribution with normal distribution. In evaluating the recommended GBM level of precision, the model parameters are estimated. A Sequential Monte Carlo technique based on student-t distribution is developed to estimate the random effects and parameters for the extended model. The SMC or particle filter based upon the student's t-distribution for the GBM model can precisely capture the aforementioned statistical characteristics of return distributions and can model and predict the fluctuation in stock prices. Through stochastic simulations and the accuracy of the models which was proven by the lower value of the MAPE, our analysis shows that the GBM model based on student-t is empirically more successful than the normal distribution.
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