Price jumping mechanism and parameter estimation based on filtered poisson process

Abstract

By observing the actual movement of asset prices, we find that there is a persistent shock impact of jumps on prices rather than a transient effect. To address this phenomenon, we propose a new jump-diffusion model that restores the process of price by assuming that its continuous changes are determined by the diffusion process, while individual jumps are inscribed by a filtered Poisson process. We also come up with estimation methods for the parameters involved in the jump process, as well as methods for identifying jumps and determining the duration of the transit impact of jumps based on the actual price series. In terms of simulations, the consistency of the estimation results is verified in detail. Finally, we select two representative indexes in the China’s stock market as empirical objects. We build the price models, perform jump tests and parameter estimation for them, and compare the results with that of the traditional multi-sample BN-s to demonstrate the validity and robustness of the proposed models and estimation methods.