Modeling financial environments using geometric fractional Brownian motion model with long memory stochastic volatility - Al Haqyan, Mohammed Kamel Mohammed (2018)
Geometric Fractional Brownian Motion (GFBM) model is widely used in financial environments. This model consists of important parameters i.e. mean, volatility, and Hurst index, which are significant to many problems in finance particularly option pricing, value at risk, exchange rate, and mortgage insurance. Most current works investigated GFBM under the assumption of its volatility that is constant due to its simplicity. However, such assumption is normally rejected in most empirical studies. Therefore, this research develops a new GFBM model that can better describe and reflect real life situations particularly in financial scenario. All parameters involved in the developed model are estimated by using innovation algorithm. A simulation study is then conducted to determine the performance of the new model. The results of simulation reveal that the proposed estimators are efficient based on the bias, variance, and mean square error. Subsequently, two theorems on existence and uniqueness of the solution for the new model and its generalisation are constructed. The validation of the developed model was then carried out by comparing with other models in forecasting adjusted prices of Standard and Poor 500, Shanghai Stock Exchange Composite Index, and FTSE Kuala Lumpur Composite Index. Empirical studies on four selected financial applications, i.e. option pricing, value at risk, exchange rate, and mortgage insurance, indicate that the new model performs better than the existing ones. Hence, the new model has strong potential to be employed as an underlying model for any financial applications that capable of reflecting the real situation more accurately.