Kittisak Chumpong, Khamron Mekchay and Sanae Rujivan

DOI: 10.14456/sjst-psu.2020.107

pp. 836 - 843

Abstract

This paper derives a simple closed-form formula for the n^th conditional moment of the Ornstein-Uhlenbeck (O-U)
process, for any positive integer n. The system of recursive ordinary differential equations (ODEs) associated with the n^th
conditional moment of the O-U process is solved analytically. We also provide practitioners a pseudocode for an algorithm to
compute the conditional moments and discuss the efficiency of our formula compared to solving the system of recursive ODEs
using the direct method.

Keywords

• O-U process
• conditional expectation
• closed-form formula