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 binary options and their integrals, we give the pricing formulae of defaultable bonds in both cases of exogenous and endogenous default recoveries and credit spread analysis .