Bayesian estimation of fractional rnstein-uhlenbeck model parameters using the sir algorithm in financial derivatives pricing

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.

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 to the MLE estimator based on RMSE and variance indices.

The results demonstrate that the Bayesian estimator provides more accurate parameter estimates than the Maximum Likelihood method. Moreover, with an increase in the degree of long-term dependency on the data, 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.

 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 estimating parameters in stochastic differential models with long-memory properties, and it opens new avenues for applying similar techniques to models like the Heston model in future research.