Estimation for a Second-Order Jump Diffusion Model from Discrete Observations: Application to Stock Market Returns

Abstract

This paper proposes a second-order jump diffusion model to study the jump dynamics of stock market returns via adding a jump term to traditional diffusion model. We develop an appropriate maximum likelihood approach to estimate model parameters. A simulation study is conducted to evaluate the performance of the estimation method in finite samples. Furthermore, we consider a likelihood ratio test to identify the statistically significant presence of jump factor. The empirical analysis of stock market data from North America, Asia, and Europe is provided for illustration.