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Solution Representations of Solving Problems for the Black-Scholes equations and Application to the Pricing Options on Bond with Credit Risk

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  • Hyong-Chol O
  • Tae-Song Kim
  • Tae-Song Choe

Abstract

In this paper is investigated the pricing problem of options on bonds with credit risk based on analysis on two kinds of solving problems for the Black-Scholes equations. First, a solution representation of the Black-Scholes equation with the maturity payoff function which is the product of the power function, normal distribution function and characteristic function is provided. Then a solution representation of a special terminal boundary value problem of the Black-Sholes equation is provided and its monotonicity is proved. The simplest case of the structural model of the credit bond is studied and its pricing formula is provided, and based on the results, the pricing model of option on corporate bond with credit risk is transformed into a terminal boundary value problem of the Black-Scholes equation with some special maturity payoff functions and the solution formula is obtained. Using it, we provide the pricing formulae of the puttable and callable bonds with credit risk.

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  • 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.
    • Handle: RePEc:arx:papers:2109.10818
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    References listed on IDEAS

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    1. 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.
    2. Hyong-Chol O & Ning Wan, 2013. "Analytical Pricing of Defaultable Bond with Stochastic Default Intensity," Papers 1303.1298, arXiv.org, revised Apr 2013.
    3. Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
    4. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    5. 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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    Cited by:

    1. 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.
    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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