Proposed a new method of moment estimator for Ornstein Uhlenbeck processes with jump noise in financial markets

Authors
Maral Aryanpour
Parisa Nabati
Urmia University of Technology
Abstract
This paper proposed a new method for parameters estimation of the Ornstein Uhlenbeck processes driven with the compound Poisson process. These processes have some applications in modeling and forecasting in financial markets. The proposed estimators are derived based on the method of the moment. In this work, the central limit theorem for the proposed estimators is also established. Numerical experiments are provided to show that the proposed method performs better in comparison with the existing methods, especially in cases when the jumps of the compound Poisson process are relatively rare. As an experimental approach, we fit the Mobarakeh Steel company data with Gamma, Pareto, and Normal Ornstein Uhlenbeck processes and estimate the parameters by using the proposed method. Finally, under these stochastic models, we simulate the volatility of the Mobarakeh Steel Company.
Keywords
Ornstein Uhlenbeck process
Levy noise
Parameter estimation
Method of moments
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