Simulation of Stochastic differential equation of geometric Brownian motion by quasi-Monte Carlo method and its application in prediction of total index of stock market and value at risk

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 pseudorandom numbers, but in quasi-Monte Carlo method, quasirandom 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.

Parameter estimation of some Kumaraswamy-G type distributions

“…For example, some recent simulation studies can be found in [1,18]. Abbasbandy and Shivanian [1] used numerical simulation based on meshless technique to study the biological population model.…”

“…Abbasbandy and Shivanian [1] used numerical simulation based on meshless technique to study the biological population model. Vajargah and Shoghi [18] used quasi-Monte Carlo method in prediction of total index of stock market and value at risk. To assess the performance of the ML and MSP estimators we conducted a small size simulation study for the Kum-W, Kum-Par and Kum-Pow distributions.…”

Performance Evaluation of Association Rule Mining with Enhanced Apriori Algorithm Incorporated with Artificial Bee Colony Optimization Algorithm

“…Kianoush Fathi Vajargah et al [25] had proposed in the predictions of total stock list, are confronted with a few parameters as they are questionable in future and they can experience changes, and this instability has a couple dangers, and for a genuine examination, the calculations ought to be performed under danger conditions. The predictions of total stock list and esteem at danger by this technique are preferable and more correct over Monte Carlo strategy.…”

Computational technique for simulating variable-order fractional Heston model with application in US stock market

“…The Black-Scholes model has been introduced based on the geometric Brownian motion to providing a closed-form pricing formula for the European options and describing the behavior of underlying asset prices [1][2][3]. The assumptions of the Black-Scholes model are unrealistic due to its inability to generate volatility satisfying the market observations, being nonnegative and mean-reverting [4][5][6].…”