Optimal Stopping for Locking a Mortgage Rate

Summary

The document frames the choice of when to lock a mortgage rate during the period before closing as an optimal stopping problem. Once locked, the borrower cannot switch back, and the objective is to choose a favorable rate from the available sequence. It compares this setup with the classical secretary problem, where a rule based on waiting through an initial portion of observations is often considered.

The author emphasizes that mortgage rates are not independent, identically distributed observations, so the classical rule may not apply directly. A random-walk model is raised as one possible description, alongside a reported claim that a related secretary problem can favor choosing the first observation. The post does not establish the assumptions behind that claim or derive an optimal strategy for mortgage rates; it asks for a reference. Its value is in identifying the modeling issue: an optimal locking rule depends on the dynamics of rates and the decision constraints.

Key ideas

• Mortgage rate locking can be modeled as an optimal stopping decision with an irreversible choice.
• The classical secretary-problem waiting rule relies on assumptions that may not fit mortgage-rate dynamics.
• A random-walk model is suggested, but the cited result’s assumptions are left uncertain.
• The document does not derive or validate a specific optimal locking strategy.

Tags

# Optimal mortgage rate strategy


# Optimal mortgage rate strategy












When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert.

This makes it a secretary problem - in the traditional problem, we would want to lock in at the lowest point after waiting $\sqrt{60}$ days. However, unlike in the traditional problem the rates are not i.i.d., so it becomes harder.

One model is to assume prices form a random walk; I've found this paper whose abstract says that the optimal strategy in random walk secretary problems is to choose the first rate, but the text is behind a pay wall so I'm not sure of all the assumptions.

Can someone point me to a reference on optimal stopping in the case of locking in mortgage rates?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.