Pricing Corporate Defaultable Bond using Declared Firm Value

TL;DR

This paper develops a PDE-based model for pricing corporate defaultable bonds considering discrete-time declared firm values and stochastic default intensities, providing explicit pricing formulas for such bonds.

Contribution

It introduces a novel PDE approach for pricing defaultable bonds with discrete declared firm values and stochastic default intensities, extending existing models.

Findings

Derived a PDE model for bond pricing with declared firm values.

Provided explicit pricing formulas for the proposed model.

Addressed PDEs with random constants and binary terminal conditions.

Abstract

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 the firm. We consider the problem for pricing of corporate defaultable bond in the case when the firm value is only declared in some fixed discrete time and unexpected default intensity is determined by the declared firm value. Here we provide a partial differential equation model for such a defaultable bond and give its pricing formula. Our pricing model is derived to solving problems of partial differential equations with random constants (de- fault intensity) and terminal values of binary types. Our main method is to use the solving method of a partial differential equation with a random constant in every subinterval and to take expectation to remove the random constants.