A closed-form formula for the conditional moments of the extended CIR process

摘要

In this paper, we derive a simple closed-form formula for the γth conditional moment of a variance process, based on the extended Cox–Ingersoll–Ross (ECIR) process, for any real number γ. The closed-form formula presented here is a result of successfully finding an exact solution for the partial differential equation, based on the ECIR process. We conduct Monte Carlo simulations to illustrate the accuracy of the current closed-form formula.