  In this work, a pricing model for a defaultable corporate bond with credit
rating migration risk is established. The model turns out to be a free boundary
problem with two free boundaries. The latter are the level sets of the solution
but of different kinds. One is from the discontinuous second order term, the
other from the obstacle. Existence, uniqueness, and regularity of the solution
are obtained. We also prove that two free boundaries are $C^\infty$. The
asymptotic behavior of the solution is also considered: we show that it
converges to a traveling wave solution when time goes to infinity. Moreover,
numerical results are presented.
