Estimation of Jump-Diffusion Processes With Shot-Noise Effects

Abstract

This paper analyses the evolution through time of stock prices considering an extension of jump diffusion processes that incorporates Shot Noise effects. This extension follows the model recently proposed by Altmann et al (2004). The shot noise process introduces a new situation in which the jump effects may fade away on the long run. Thus, this model generalizes other specifications of jump diffusion models as, for instance, Merton (1976) and, then, implies a major flexibility of the model. In addition, many statistical distributions appear as marginal distributions for simple shot-noise processes. This paper provides a general expression for the distribution of the process, which is crucial for its estimation. We also present an estimation procedure based on spectral analysis and perform an exhaustive Monte Carlo study. Finally, an empirical application to real stock prices data is implemented reflecting evidence of shot noise effects in many of the series under analysis.

Keywords: Shot Noise, Characteristic Function, Spectral Density

JEL Classification: C13, C15, C22, C52