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Higher Order Binaries with Time Dependent Coefficients and Two Factors - Model for Defaultable Bond with Discrete Default Information

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  • Hyong-Chol O
  • Yong-Gon Kim
  • Dong-Hyok Kim

Abstract

In this article, we consider a 2 factors-model for pricing defaultable bond with discrete default intensity and barrier where the 2 factors are stochastic risk free short rate process and firm value process. We assume that the default event occurs in an expected manner when the firm value reaches a given default barrier at predetermined discrete announcing dates or in an unexpected manner at the first jump time of a Poisson process with given default intensity given by a step function of time variable. Then our pricing model is given by a solving problem of several linear PDEs with variable coefficients and terminal value of binary type in every subinterval between the two adjacent announcing dates. Our main approach is to use higher order binaries. We first provide the pricing formulae of higher order binaries with time dependent coefficients and consider their integrals on the last expiry date variable. Then using the pricing formulae of higher binary options and their integrals, we give the pricing formulae of defaultable bonds in both cases of exogenous and endogenous default recoveries and credit spread analysis.

Suggested Citation

  • Hyong-Chol O & Yong-Gon Kim & Dong-Hyok Kim, 2013. "Higher Order Binaries with Time Dependent Coefficients and Two Factors - Model for Defaultable Bond with Discrete Default Information," Papers 1305.6868, arXiv.org, revised Jun 2013.
    • Handle: RePEc:arx:papers:1305.6868
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    Cited by:

    1. Hyong-chol O & Song-gon Jang & Il-Gwang Jon & Mun-Chol Kim & Gyong-Ryol Kim & Hak-Yong Kim, 2015. "The Binomial Tree Method and Explicit Difference Schemes for American Options with Time Dependent Coefficients," Papers 1505.04573, arXiv.org, revised Aug 2018.
    2. Hyong-Chol O & Dae-Sung Choe, 2019. "Pricing Formulae of Power Binary and Normal Distribution Standard Options and Applications," Papers 1903.04106, arXiv.org.
    3. 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.
    4. Hyong-Chol O. & Jong-Chol Kim & Il-Gwang Jon, 2017. "Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon," Papers 1709.06517, arXiv.org, revised Aug 2018.

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