Risk-Neutral Measure for an Ornstein–Uhlenbeck Process

Summary

The question asks whether converting a mean-reverting Ornstein–Uhlenbeck (OU) process to a risk-neutral measure works by replacing its drift with the risk-free rate, as is often done for geometric Brownian motion. The response points to a discussion that describes the risk-neutral version of the OU setup as a simple geometric Brownian motion and refers readers to a paper for the explanation.

The note offers no derivation, assumptions, or pricing example, so it is only a pointer rather than a complete change-of-measure method. It does not establish that the drift-substitution rule applies generally or explain how the result depends on the modeled variable and traded assets. Readers would need the cited source to assess the claim and its scope.

Key ideas

• The question concerns changing the measure for a mean-reverting OU process.
• The response claims that the risk-neutral version becomes a simple geometric Brownian motion.
• The answer points to an external paper but gives no derivation or stated assumptions.

Tags

# How to change to risk neutral measure in a mean reversion process?


# How to change to risk neutral measure in a mean reversion process?












For example, in the Ornstein-Uhlenbeck process do I just replace the drift term with the risk free rate, like in the GBM case?

## Answer by airguru (score 2)

https://quant.stackexchange.com/a/22193

Risk neutral version of O-U process is apparently a simple GBM. See explanation here, http://web.mit.edu/wangj/www/pap/LoWang95.pdf specifically section II.

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