We study Danish fixed-rate mortgage contracts, which are identical to those in the United States except that borrowers may repurchase their mortgages at market value.

Using Danish administrative data, we show that households actively buy back debt when mortgage prices fall below par and that household mobility is largely insensitive when existing mortgage rates are below prevailing market rates --- unlike in the United States, where moving rates fall sharply as rates rise.

We develop an equilibrium model that explains these patterns and show that introducing a repurchase-at-market option into U.S. mortgages substantially reduces interest-rate-induced lock-in with limited effects on equilibrium mortgage rates.