Free boundary problem pricing defaultable corporate bonds with multiple credit rating migration risk and stochastic interest rate

Huang, Zhehao; Miao, Yingting; Wang, Zhenzhen

doi:10.3934/math.2020495

Cited by 2 publications

(2 citation statements)

References 32 publications

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“…Wu and Liang [46] provided some numerical results for multiple credit rating migration problems. More papers on credit rating migration modeling by the structural approach are Wu and Liang [47], Wu et al [48], Wang et al [49], Huang et al [50,51], Liang and Zhou [52], and so forth.…”

Section: Literature Reviewmentioning

confidence: 99%

Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration

Huang

Wang

2020

Mathematics

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Credit risk modeling by debt pricing has been a popular theme in both academia and practice since the subprime crisis. In this paper, we devote our study to the indifferent price of a corporate bond with credit risk involving both default risk and credit rating migration risk in an incomplete market. The firm’s stock and a financial index on the market as tradable assets are introduced to hedge the credit risk, and the bond price is determined by the indifference of investors’ utilities with and without holding the bond. The models are established under the structural framework and result in Hamilton–Jacobi–Bellman (HJB) systems regarding utilities subject to default boundary and multiple migration boundaries. According to dynamic programming theory, closed-form solutions for pricing formulas are derived by implementing an inverted iteration program to overcome the joint effect of default and multiple credit rating migration. Therefore, with the derived explicit pricing formulas for the corporate bond, the models can be easily applied in practice, and investors can generate their strategies of hedging the credit risk by easily analyzing the impacts of the parameters on the bond price.

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Section: Literature Reviewmentioning

confidence: 99%

Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration

Huang

Wang

2020

Mathematics

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“…Zhao [4] studied the wave speed of a stochastic KPP equation driven by white noise. Huang and Wang [5][6][7][8][9] investigated the asymptotic behavior of a stochastic reaction-diffusion equation driven by various noises. Indeed, a way to deal with the coupling terms is the crux in the research of travelling wave solution of stochastic reaction-diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of Stochastic Reaction–Diffusion Equations

Wen,

Wang,

Liu

et al. 2024

Mathematics

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In this paper, we concentrate on the propagation dynamics of stochastic reaction–diffusion equations, including the existence of travelling wave solution and asymptotic wave speed. Based on the stochastic Feynman–Kac formula and comparison principle, the boundedness of the solution of stochastic reaction–diffusion equations can be obtained so that we can construct a sup-solution and a sub-solution to estimate the upper bound and the lower bound of wave speed.

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Free boundary problem pricing defaultable corporate bonds with multiple credit rating migration risk and stochastic interest rate

Cited by 2 publications

References 32 publications

Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration

Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration

Asymptotic Behavior of Stochastic Reaction–Diffusion Equations

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