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 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 order binaries with time dependent coefficients and consider their integrals on the last expiry date variable. Then using the pricing formulae of higher binary options .