Some Properties of CIR Processes

Abstract

This article derives some properties of variants of squared Bessel processes known as CIR processes in the finance literature. We derive the transition probability density function of a square-root process and compute the resolvent density of CIR processes. As a consequence, we derive the density of CIR processes sampled at an independent exponential time. Moreover, we derive explicit expressions of the Laplace transforms (LTs) of first hitting times by martingale methods.

Keywords:

• Barrier options
• CIR processes
• Hitting times
• Resolvent

MSC Classification (2000):

• 60E05
• 60J60