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

Hyong-Chol, O; Kim, Yong-Gon; Kim, Dong-Hyok

doi:10.2139/ssrn.2337865

SSRN Journal

2013

DOI: 10.2139/ssrn.2337865

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

O Hyong-Chol

Yong-Gon Kim

Dong-Hyok Kim

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Cited by 3 publications

References 14 publications

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General properties of solutions to inhomogeneous Black–Scholes equations with discontinuous maturity payoffs

Hyong-Chol¹,

Jo²,

Kim³

2016

Journal of Differential Equations

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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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General properties of solutions to inhomogeneous Black–Scholes equations with discontinuous maturity payoffs

Hyong-Chol¹,

Jo²,

Kim³

2016

Journal of Differential Equations

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Analytical pricing of defaultable discrete coupon bonds in unified two-factor model of structural and reduced form models

Hyong-Chol¹,

Kim²,

Pak³

2014

Journal of Mathematical Analysis and Applications

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Analytical Pricing of Defaultable Discrete Coupon Bonds in Unified Model of Structural and Reduced Form Models (Two-Factor Model)

2013

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: Pricing formulae for defaultable corporate bonds with discrete coupons under consideration of the government taxes in the united model of structural and reduced form models are provided. The aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in [1]) into a comprehensive unified model of structural and reduced form models. Here we consider the one factor model and the two factor model. In the one factor model the bond holders receive the deterministic coupon at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under constant short rate. In the two factor model the bond holders receive the stochastic coupon (discounted value of that at the maturity) at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under stochastic short rate. The expected default event occurs when the equity value is not enough to pay coupon or debt at the coupon dates or maturity and unexpected default event can occur at the first jump time of a Poisson process with the given default intensity provided by a step function of time variable. We consider the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons and consider its duration and the effect of the government taxes.

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

Cited by 3 publications

References 14 publications

General properties of solutions to inhomogeneous Black–Scholes equations with discontinuous maturity payoffs

General properties of solutions to inhomogeneous Black–Scholes equations with discontinuous maturity payoffs

Analytical pricing of defaultable discrete coupon bonds in unified two-factor model of structural and reduced form models

Analytical Pricing of Defaultable Discrete Coupon Bonds in Unified Model of Structural and Reduced Form Models (Two-Factor Model)

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