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

Hyong Chol O, Dae Song Choe and Gyong-Dok Rim

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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.

Date: 2022-03
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