Parameters estimation for jump-diffusion process based on low and high frequency data

Abstract

In this thesis, we develop some parameter estimation methods of jump-diffusion process. The originality of the thesis lies in the fact that the developed estimation methods are different from those commonly-used approaches. This thesis consists of two parts. In the first part, estimation method for continuous state branching process with immigration (hereafter, CBI) is proposed, which is based on the weighted conditional least square estimators (WCLSE). It is remarkable that the Cox-Ingersoll-Ross model with jumps (JCIR) in the studies of interest rate is a simplified version of our CBI process. Our developed method provides new perspective in parameter estimation for JCIR model. The strength of the method is that it avoids computationally expensive numerical integration which is used in many extant estimation methods. In the second part, particle Markov chain Monte Carlo method is applied to the estimation of a parametric model for ultra-high frequency stock price data, whereas most existing studies mainly focus on nonparametric estimation methods. Our method has two special features: on the one hand, it can estimate all parameters in the jump-diffusion model whereas nonparametric methods can only provide volatility estimation; on the other hand, it can effectively estimate volatility generated by diffusion component under the influence of jumps with market microstructure noise. Detailed simulation studies are implemented for both developed methods to evaluate their estimation performance. Results indicate that both these methods lead to reasonable estimations for parameters in the models.