Analytical Pricing of 2 Factor Structural PDE model for a Puttable Bond with Credit Risk

TL;DR

This paper develops an analytical 2-factor PDE model for pricing puttable bonds with credit risk, deriving explicit formulas and analyzing the monotonicity of bond prices.

Contribution

It introduces a novel 2-factor structural PDE framework for pricing credit risky puttable bonds and derives explicit analytical formulas under specific conditions.

Findings

Derived explicit pricing formulas for puttable bonds with credit risk.

Proved the monotonicity of bond prices with respect to firm value.

Transformed the model into a Black-Scholes type equation for easier analysis.

Abstract

In this paper is proposed a 2 factor structural PDE model of pricing puttable bond with credit risk and derived the analytical pricing formula. To this end, first, a 2 factor structural (PDE) model of pricing zero coupon bond with credit risk is provided, the analytical pricing formula is derived under some conditions for default boundary and default recovery, and the strict monotonicity of the bond price function with respect to the firm value variable is proved. Then a (2 factor) pricing model of the option on zero coupon bond with credit risk is provided and under some condition on the exercise price its analytical pricing formula is derived by transforming the 2 factor model into a terminal boundary value problem for Black-Scholes equation with time dependent coefficient using zero coupon bond as numeraire. Using it, we provide the pricing formulae of the puttable and callable bonds with credit risk.