SONGKLANAKARIN JOURNAL OF SCIENCE & TECHNOLOGY

Volume 42, No. 04, Month JULY, Year 2020, Pages 836 - 843

A simple closed-form formula for the conditional moments of the ornstein-uhlenbeck process

Kittisak Chumpong , Khamron Mekchay and Sanae Rujivan

Abstract Download PDF

This paper derives a simple closed-form formula for the nth 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 nth 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

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