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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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    $\begingroup$ Note that you can often break the lock for a fee (e.g. 1/8). $\endgroup$ – Joshua Ulrich May 20 '13 at 16:54

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