Journal of Quality Engineering and Management

Bayesian estimation of fractional Ornstein-Uhlenbeck model parameters using the sir algorithm in financial derivatives pricing

Document Type : Original Article

Authors

Parviz Nasiri 1
Amir Haj Salmani 1
Mahdiyeh Tahmasbi 2

1 Department of Statistics, Payam Noor University, Tehran, Iran.

2 Department of Mathematics, Tarbiat Modares University, Tehran, Iran.

https://doi.org/10.48313/jqem.2025.513308.1507
Abstract
Purpose: This paper aims to accurately estimate the parameters of the fractional Ornstein-Uhlenbeck model using the Bayesian method and the SIR simulation algorithm and to compare its performance with the Maximum Likelihood Estimation (MLE) method in the context of stochastic differential models with long-memory properties. The paper also seeks to evaluate the efficiency of the Bayesian approach in similar models, particularly in analyzing financial data with long-term dependencies.
Methodology: In this study, the parameters of the fractional Ornstein-Uhlenbeck model are estimated for the first time using the Bayesian method, with appropriate prior distributions and the SIR algorithm employed for simulation. The efficiency of the Bayesian estimator is compared with that of the MLE estimator using RMSE and variance indices.
Findings: The results demonstrate that the Bayesian estimator provides more accurate parameter estimates than the Maximum Likelihood method. Moreover, as the degree of long-term data dependence increases, the accuracy of estimates improves under both methods; however, the Bayesian approach consistently outperforms the MLE. Additionally, the parameter σ is estimated with higher precision compared to the parameters k and μ.
Originality/Value: The originality of this paper lies in the application of the SIR algorithm to estimate the parameters of the fractional Ornstein-Uhlenbeck model. This approach has not been previously explored. This innovation represents a significant contribution to the application of Bayesian methods for parameter estimation in stochastic differential models with long-memory properties, and it opens new avenues for applying similar techniques to models such as the Heston model in future research.

Keywords

Long-term memory models
Heston model
Fractional Ornstein Uhlenbeck model
Fractional model
SIR algorithm
Bayesian estimation
Maximum likelihood method
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Journal of Quality Engineering and Management
Volume 14, Issue 3
Autumn 2024
Pages 217-223

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