  In this article, we study the problem of pricing defaultable bond with
discrete default intensity and barrier under constant risk free short rate
using higher order binary options and their integrals. In our credit risk
model, the risk free short rate is a constant and the default event occurs in
an expected manner when the firm value reaches a given default barrier at
predetermined discrete announcing dates or in an unexpected manner at the first
jump time of a Poisson process with given default intensity given by a step
function of time variable, respectively. We consider both endogenous and
exogenous default recovery. Our pricing problem is derived to a solving problem
of inhomogeneous or homogeneous Black-Scholes PDEs with different coefficients
and terminal value of binary type in every subinterval between the two adjacent
announcing dates. In order to deal with the difference of coefficients in
subintervals we use a relation between prices of higher order binaries with
different coefficients. In our model, due to the inhomogenous term related to
endogenous recovery, our pricing formulae are represented by not only the
prices of higher binary options but also the integrals of them. So we consider
a special binary option called integral of i-th binary or nothing and then we
obtain the pricing formulae of our defaultable corporate bond by using the
pricing formulae of higher binary options and integrals of them.
