Abstract
In the prediction of total stock index, we are faced with some parameters as they are uncertain in future and they can undergo changes, and this uncertainty has a few risks, and for a true analysis, the calculations should be performed under risk conditions. One of the evaluation methods under risk and uncertainty conditions is using geometric Brownian motion random differential equation and simulation by Monte Carlo and quasi-Monte Carlo methods as applied in this study. In Monte Carlo method, pseudo-random sequences are used to generate pseudo-random numbers, but in quasi-Monte Carlo method, quasi-random sequences are used with better uniformity and more rapid convergence compared with pseudo-random sequences. The predictions of total stock index and value at risk by this method are better and more exact than Monte Carlo method. This study at first evaluates random differential equation of geometric Brownian motion and its simulation by quasi-Monte Carlo method, and then its application in the predictions of total stock market index and value at risk can be evaluated.
Highlights
Like other fields of management knowledge and its application, risk management applies knowledge, principles, and specific rules to estimate predictions and achieve predefined goals
In the prediction of total stock index, we are faced with some parameters as they are uncertain in future and they can undergo changes, and this uncertainty has a few risks, and for a true analysis, the calculations should be performed under risk conditions
In Monte Carlo method, pseudo-random sequences are used to generate pseudorandom numbers, but in quasi-Monte Carlo method, quasirandom sequences are used with better uniformity and more rapid convergence compared with pseudo-random sequences
Summary
Like other fields of management knowledge and its application, risk management applies knowledge, principles, and specific rules to estimate predictions and achieve predefined goals. As assets do not follow normal distribution under these conditions, this study applies nonparametric and Monte Carlo and quasi-Monte Carlo simulation techniques In this method, by simulation of samples through computer and MATLAB software and random differential equation of geometric Brownian motion, the prediction is performed. Math Sci (2015) 9:115–125 quasi-Monte Carlo simulation methods to calculate total index and VAR of stock market to quantify the maximum probable loss with the lowest percentage error for the investment in stock market by considering the volatilities in the market. This issue is of great importance for stock managers. A comparison is made between quasi-random sequences and pseudo-random sequences, definitions of the terms that are used regarding stock market are given, and conclusions are drawn
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