Properties of Doubly Stochastic Poisson Process with affine intensity

TL;DR

This paper analyzes the properties of a Doubly Stochastic Poisson Process with affine diffusion intensities, deriving analytical distributions and applying Kalman filtering to estimate parameters from high-frequency transaction data.

Contribution

It provides explicit analytical expressions for DSPP distributions with affine intensity processes and demonstrates parameter estimation using Kalman filtering in a specific case.

Findings

Derived analytical distribution functions for DSPP with affine intensities.

Applied Kalman filtering to estimate model parameters from real data.

Validated the model's applicability to high-frequency financial data.

Abstract

This paper discusses properties of a Doubly Stochastic Poisson Process (DSPP) where the intensity process belongs to a class of affine diffusions. For any intensity process from this class we derive an analytical expression for probability distribution functions of the corresponding DSPP. A specification of our results is provided in a particular case where the intensity is given by one-dimensional Feller process and its parameters are estimated by Kalman filtering for high frequency transaction data.