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: Pricing formulae for defaultable corporate bonds with discrete coupons under consideration of the government taxes in the united model of structural and reduced form models are provided. The aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in [1]) into a comprehensive unified model of structural and reduced form models. Here we consider the one factor model and the two factor model. In the one factor model the bond holders receive the deterministic coupon at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under constant short rate. In the two factor model the bond holders receive the stochastic coupon (discounted value of that at the maturity) at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under stochastic short rate. The expected default event occurs when the equity value is not enough to pay coupon or debt at the coupon dates or maturity and unexpected default event can occur at the first jump time of a Poisson process with the given default intensity provided by a step function of time variable. We consider the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons and consider its duration and the effect of the government taxes.

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In this article, we consider a 2 factors-model for pricing defaultable bonds with discrete default intensity and barrier where the 2 factors are a stochastic risk free short rate process and firm value process. We assume that 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. Then our pricing model isgiven by a solving problem of several linear PDEs with variable coefficients and terminal value of binary type in every subinterval between the two adjacent announcing dates. Our main approach is to use higher order binaries. We first provide 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 and their integrals, we give the pricing formulae of defaultable bonds in both cases of exogenous andendogenous default recoveries and perform credit spread analysis.

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