Optimization of estimates and comparison of their efficiency under stochastic methods and its application in financial models

Subject Areas : Financial and Economic Modelling

Kianoush  Fathi vajargah ¹ (Department of Statistics, Islamic Azad University, North branch, Tehran, Iran,)
Hamid  Mottaghi Golshan ² (Department of Mathematics, Shahriar Branch, Islamic Azad University, Shahriar, Iran)
Abbas  Arjomandfar ³ (Department of Mathematics, Yadegar-e-Imam Khomeini (RAH), Shahrerey Branch, Islamic Azad University, Tehran, Iran)

Received: 2021-12-06 Accepted : 2022-04-04 Published : 2023-07-01

Keywords: random sequence, Quasi-random sequence, Stochastic Differential Equation, (Quasi) Monte Carlo simulation,

Abstract :

In this paper, first, the stochastic differential equations are introduced as well as the definition and basic theories about Monte Carlo and quasi-Monte Carlo and Sobel and Halton sequences are expressed. Indeed, we introduce and use simulations under these methods to compare the efficiency of the solutions, which the results show that the approximation of the resulting Sobel sequence is much better than other stochastic methods. The comparison of the efficiency of random and quasi-random methods, the geometric Brownian movement and the price index of Tehran stock (equal weight and weight-value) is studied. The results show that the quasi-Monte Carlo method is better than other methods.

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