Before revision:  Our main method to give the pricing of defaultable bonds is to transform several PDEs for pricing in every subinterval between the two adjacent announcing dates into a pricing problem of a higher order binary option using several changes of variable and unknown function including change of numeraire and then to use the pricing  formulae of higher binary options  .
After revision:  Our main approach is to use higher order binaries. We first provide the pricing formulae of higher binary options .