|Title:||Parameters estimation for jump-diffusion process based on low and high frequency data|
Diffusion -- Mathematical models.
Monte Carlo method.
Hong Kong Polytechnic University -- Dissertations
|Department:||Department of Applied Mathematics|
|Pages:||viii, 94 p. : ill. ; 30 cm.|
|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.|
As a bona fide Library user, I declare that:
- I will abide by the rules and legal ordinances governing copyright regarding the use of the Database.
- I will use the Database for the purpose of my research or private study only and not for circulation or further reproduction or any other purpose.
- I agree to indemnify and hold the University harmless from and against any loss, damage, cost, liability or expenses arising from copyright infringement or unauthorized usage.
By downloading any item(s) listed above, you acknowledge that you have read and understood the copyright undertaking as stated above, and agree to be bound by all of its terms.
Please use this identifier to cite or link to this item: