Akademik Veri Yönetim Sistemi
6th International Conference on Computational Mathematics and Engineering Sciences / 20-22 May. 2022, Ordu – Turkey, Ordu, Türkiye, 20 - 22 Mayıs 2022, cilt.1, sa.1, ss.257
In this study, GOLD data versus USD is investigated by Stochastic Differential
Equation Modeling (SDEM). First of all, Square Root Process, Geometric Brownian Motion
(GBM), Vasicek Model (VAS), and Cox-Ingersoll-Ross (CIR) models have selected from the
most preferred models in finance. Then, the parameters of the mentioned SDE models have
estimated using the quasi maximum likelihood method. Secondly, It has been given the pvalue
for the Kolmogorov-Smirnov test that checks if the empirical and theoretical
distribution are the same to see the goodness of fit of the model. Accordingly, all selected
models fit well with the given data. After that, model selection has been made among these 4
compatible models according to AIC and BIC criteria. Therefore, for the given data, the VAS
model is the most appropriate model according to both criteria. Finally, by using the VAS
model, which has been chosen as the most appropriate model, and applying Euler-Maruyama
Approximation Method future simulation trajectories of 100 steps between 25.04.2022 and
25.04.2023 have been obtained. Gold opening data with the symbol GC=F between
02.01.2020 and 25.04.2022 have obtained with the help of https://finance.yahoo.com/ link,
with the YUIMAGUI interface of the RSTUDIO program and all results have also made by
using YUIMAGUI. These results are also corroborated by graphical representation.
Keywords: stochastic differential equation , quasi maximum likelihood, Euler-Maruyama
aroximation method,square root process, CIR, GBM, VAS, YUIMAGUI.