Exact Simulation of Point Processes with Stochastic Intensities

Authors:
K. Giesecke;H. Kakavand;M. Mousavi
Affiliations:
Department of Management Science and Engineering, Stanford University, Stanford, California 94305;The Perot Group;Department of Management Science and Engineering, Stanford University, Stanford, California 94305
Venue:
Operations Research
Year:
2011

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Abstract

Point processes with stochastic arrival intensities are ubiquitous in many areas, including finance, insurance, reliability, health care, and queuing. They can be simulated from a Poisson process by time scaling with the cumulative intensity. The paths of the cumulative intensity are often generated with a discretization method. However, discretization introduces bias into the simulation results. The magnitude of the bias is difficult to quantify. This paper develops a sampling method that eliminates the need to discretize the cumulative intensity. The method is based on a projection argument and leads to unbiased simulation estimators. It is exemplified for a point process whose intensity is a function of a jump-diffusion process and the point process itself. In this setting, the method facilitates the exact sampling of both the point process and the driving jump-diffusion process. Numerical experiments demonstrate the effectiveness of the method.