In the talk, I present different properties of rating migration process C given by Cox process. Among others I derive some useful conditional expecttions of a F-predicatble bounded stochastic process Z_t taking at default time τ, i.e. Z_τ, given pre-default state C_{τ -} and t≤τ≤ u under F_t V F_t^c.

Applications of these results to problem of pricing defaultable bonds with fractional recovery of par value with rating migration and to problem of pricing credit default swaps will be considered.