Subdiffusive Ornstein-Uhlenbeck Processes and Applications to Finance

Abstract

In this paper we analysis the subdiffusive structure of ISE 100 index price evaluation using the subordinated Ornstein-Uhlenbeck process. We use the subordinated Langevin equation approach to obtain a model of index prices. We use the inverse tempered a stable distribution as a subordinator process. The subordinated Langevin equation approach is parallel to role played by Riemann-Liouville operator in fractional Fokker-Planck equation. Our aim to enhance the understanding of logarithmic asset returns behavior. We investigated the evolution of the subordinated Ornstein-Uhlenbeck process. The studied model combines the mean-reverting behavior, long range dependence and trapping events properties of index prices. To assess the capabilities of the model, we applied the model to the historical price data of the ISE100 index. The obtained results suggest that long range memory, trapping events, volatility clustering and fat tails and anomalous subdiffusive properties of interested index prices are captured by the proposed model.