Pricing Corporate Defaultable Bond with Fixed Discrete Declaration Time of Firm Value

We study the pricing problem for corporate defaultable bond from the viewpoint of the investors outside the firm that could not exactly know about the information of firm. We consider the pricing of corporate defaultable bond in the case that the firm value and default barrier just can be observed in some fixed discrete time and unexpected default intensity is determined by the declared firm value. Here we provide a PDE model for such a defaultable bond and give some pricing formula of the defaultable bond. Our pricing model is derived to a solving problem of PDE with random constant default intensity and binary terminal value. Our main method is to use the solving method of PDE for bond pricing with constant default intensity in every subinterval and to take expectation to remove some random constants. Our PDE model has no any affine structural solution and we find its solution using Fourier transformation method