Comparison of Stochastic Sampling and Application in Financial Mathematics: Evidence from the European-Asian Option Markets

Subject Areas : International Journal of Finance, Accounting and Economics Studies

Kianoush Fathi vajargah ¹ , Hossein Eslami Mofidabadi ²

1 - Department of Statistics Islamic Azad University, North branch Tehran, Iran
2 - Assistant Professor, Department of Accounting and Management, Shahryar Branch, Islamic Azad University, Shahryar, Iran

Received: 2021-05-28 Accepted : 2021-09-25 Published : 2022-04-19

Keywords: financial mathematics, application method, stochastic sampling method,

Abstract :

Purpose: The primary purpose of this research is to investigate stochastic sampling and application in financial mathematics.Methodology: Describing Monte Carlo and quasi-Monte Carlo methods in high-dimensional integrals and comparing them with each other. Finally, an example of an application Brownian bridge with quasi-Monte Carlo for financial mathematics we display. In the first part, we have shown that sequences Quasi-Monte Carlo method is a better method of Monte Carlo. Concerning the calculations on dimension reduction techniques under the Sobol sequence (Quasi-Monte Carlo Method), the ratio of variables taken from the two first variables under the Standard Method decreases when d is increased.Finding: BB and PCA are almost equal. As a result, most of the variance in these two methods are dedicated to the tiny initial dimensions. Hence, BB and PCS can significantly decrease the dimension and use the low discrepancy chains' main components. Since PCA performs better than BB, the PCA is a more efficient method than SM and BB.