Any other type of fixed-income instrument does that? I know callable/putable bonds maybe do.
when rates fall - MBS will be refinanced. that means that the issuer of the MBS gets returned the entire funds invested and he has to reinvest those at the lower rates. in addition he does not get the full “interest” that he was supposed to have received as a result of the refinancing. - this causes the contingent claim risk.
callable bonds too exhibit contingent claim risk - since the payments cap out at the strike - and do not rise like the regular bond. (negative convexity effect).