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

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  • Hyong Chol O
  • Dae Song Choe
  • Gyong-Dok Rim

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.

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  • Hyong Chol O & Dae Song Choe & Gyong-Dok Rim, 2022. "Analytical Pricing of 2 Factor Structural PDE model for a Puttable Bond with Credit Risk," Papers 2203.05719, arXiv.org.
    • Handle: RePEc:arx:papers:2203.05719
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    File URL: http://arxiv.org/pdf/2203.05719
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    References listed on IDEAS

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    1. Hyong-Chol O & Tae-Song Kim & Tae-Song Choe, 2021. "Solution Representations of Solving Problems for the Black-Scholes equations and Application to the Pricing Options on Bond with Credit Risk," Papers 2109.10818, arXiv.org, revised Nov 2021.
    2. Zhang, Kun & Liu, Jing & Wang, Erkang & Wang, Jin, 2017. "Quantifying risks with exact analytical solutions of derivative pricing distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 757-766.
    3. Hyong-Chol O & Ning Wan, 2013. "Analytical Pricing of Defaultable Bond with Stochastic Default Intensity," Papers 1303.1298, arXiv.org, revised Apr 2013.
    4. Hyong Chol O & Tae Song Kim, 2020. "Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach," Papers 2007.01511, arXiv.org.
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    1. Hyong-Chol O & Tae-Song Kim & Tae-Song Choe, 2021. "Solution Representations of Solving Problems for the Black-Scholes equations and Application to the Pricing Options on Bond with Credit Risk," Papers 2109.10818, arXiv.org, revised Nov 2021.
    2. Hyong-Chol O & Tae-Song Choe, 2022. "General properties of the Solutions to Moving Boundary Problems for Black-Sholes Equations," Papers 2203.05726, arXiv.org.
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    4. Khalique, Chaudry Masood & Motsepa, Tanki, 2018. "Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 871-879.
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