Fractions with Hull-White Operations
DOI:
https://doi.org/10.36322/jksc.178(B).21528Keywords:
random process, stochastic differential equations, fractional Brownian motion, Hull-White modelAbstract
This research dealt with presenting the Hull-White process using fractional Brownian motion, as fractional Brownian motion is characterized by its better representation of data that represents a time series with long-term reliability, especially financial and economic data. The process of fractional Brownian motion includes, in its mathematical form, the Hurst parameter (H), which represents the long memory parameter, as it is determined through its values whether it behaves characterized as (Short-Term), (Long-Term). The Hull-White model is considered As an extension of the Vasicek and CIR model, the MLE method was used to estimate these models, thus obtaining the best model for these data based on the analysis of real data representing stock prices in the stock market in Iraq, where this data was converted into interest rates to suit the nature of the three models. The studied data showed that they accurately represent the average return process. In addition, it was found that the Hull-White model is the best model to represent these data using the AIC standard.
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