Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon

TL;DR

This paper provides stability conditions for an explicit finite difference scheme applied to a complex 2-factor PDE model of corporate bonds, enabling numerical pricing, credit spread, and duration analysis.

Contribution

It introduces stability conditions for an explicit finite difference scheme for a unified 2-factor bond pricing model with mixed derivatives.

Findings

Derived stability conditions for the explicit scheme.

Numerically computed bond prices under stable conditions.

Analyzed credit spread and duration based on numerical results.

Abstract

Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's structural model [1] for discrete coupon bonds into a unified 2 factor model of structural and reduced form types and we study a numerical analysis for it by explicit finite difference scheme. These equations are parabolic equations with 3 variables and they include mixed derivatives, so the explicit finite difference scheme is not stable in general. We find conditions for the explicit finite difference scheme to be stable, in the case that it is stable, numerically compute the price of the bond and analyze its credit spread and duration.