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