Stochastic Differential Equation Modeling for Gold Data With YUIMAGUI

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Özdemir Çalıkuşu S., Erdoğan F.

6th International Conference on Computational Mathematics and Engineering Sciences / 20-22 May. 2022, Ordu – Turkey, Ordu, Turkey, 20 - 22 May 2022, vol.1, no.1, pp.257

  • Publication Type: Conference Paper / Summary Text
  • Volume: 1
  • City: Ordu
  • Country: Turkey
  • Page Numbers: pp.257
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

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.