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

In this paper, we derive a simple closed‐form formula for the ${\gamma }^{\text{th}}$ conditional moment of a variance process, based on the extended Cox–Ingersoll–Ross (ECIR) process, for any real number $\gamma$ . 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.