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General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application

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  • Hyong-Chol O
  • Ji-Sok Kim

Abstract

We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security pricing. In particular, we focus on finding representation of the gradient (with respect to the stock price variable) of solutions to the terminal value problems with discontinuous terminal payoffs or inhomogeneous terms. Such terminal value problems are often encountered in pricing problems of compound-like options such as Bermudan options or defaultable bonds with discrete default barrier, default intensity and endogenous default recovery. Our results are applied in pricing defaultable discrete coupon bonds.

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  • Hyong-Chol O & Ji-Sok Kim, 2013. "General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application," Papers 1309.6505, arXiv.org, revised Sep 2013.
    • Handle: RePEc:arx:papers:1309.6505
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    References listed on IDEAS

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    7. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, "undated". "General Properties of Option Prices (Revision of 11-95) (Reprint 058)," Rodney L. White Center for Financial Research Working Papers 1-96, Wharton School Rodney L. White Center for Financial Research.
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    Cited by:

    1. 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.
    2. Vahidreza Yousefi & Siamak Haji Yakhchali & Jolanta Tamošaitienė, 2019. "Application of Duration Measure in Quantifying the Sensitivity of Project Returns to Changes in Discount Rates," Administrative Sciences, MDPI, vol. 9(1), pages 1-14, February.
    3. Hyong-Chol O & Dae-Sung Choe, 2019. "Pricing Formulae of Power Binary and Normal Distribution Standard Options and Applications," Papers 1903.04106, 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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