Weak Convergence of Path-Dependent SDEs in Basket Credit Default Swap Pricing with Contagion Risk

In this paper, we study the basket CDS pricing with two defaultable counterparties based on the reduced-form model. The default jump intensities of the reference firms and counterparties are all assumed to follow the mean-reverting constant elasticity of variance (CEV) processes. Taking the Vasicek process which is a special case of CEV process as an example, the approximate analytic solutions of the joint survival probability density, the probability densities of the first default and the first two defaults can be solved by using PDE method. In addition, we also extend the Vasciek process to the Vasciek process with cojumps and obtain the approximate closed-form solutions of the relevant default probability densities. Then with the expressions of the probability densities, we can get the formula of the basket CDS price with two defaultable counterparties. In the numerical analysis, we do sensitivity analysis and compare the basket CDS prices under our model with that with only one defaultable counterparty. The numerical results show that our model can be applied into practice.

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“…A(t; s) and B k (t; s) have been solved by (23). Substitute the above formula into (27) to get two ODEs as follows…”

Section: Basket Cds Pricing With the Vasicek Processesmentioning

confidence: 99%

“…Gu and Liu [22] established the attenuation model for the contagious risk and derived the pricing formula of CDS in the fractional dimension environment. Huang and Song [23] priced the basket CDS with counterparty risk under a multi-name contagion model.…”

Section: Introductionmentioning

confidence: 99%

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Chen

Xing

2022

Discrete Dynamics in Nature and Society

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“…The model they proposed exhibited significant explanatory power for the cross-sectional regression of market CDS. Huang et al (Huang et al, 2017) employed stochastic differential equations (SDEs) to basket CDS pricing with contagion risk. They found sufficient conditions for the convergence of functionals associated with approximate solutions of certain path-dependent SDEs.…”

Section: Literature Review For Cds Valuationmentioning

confidence: 99%

Valuing credit default swaps in uncertain environments

2018

2018 4th International Conference on Innovative Development of E-Commerce and Logistics (ICIDEL 2018)

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The credit default swap is an important instrument in the financial market. At present, the valuation of credit default swaps is based on probability theory. In this paper, we propose a pricing formula for the credit default swap of corporate bonds from the perspective of a non-probabilistic method derived from uncertainty theory. In particular, we relate the corporate stock price to its solvency and use this relationship to develop the pricing formula. In addition, we derive two valuation models for CDS under two classic uncertain stock models. The valuation models are then compared based on their properties.

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“…Leung and Kwok [20] perform valuation of CDS with counterparty risk using the reduced form framework with inter-dependent default correlation. Huang and Song [15] priced the basket CDS with counterparty risk under a multi-name contagion model. Some scholars used copula function to describe the default correlation between the reference asset and counterparty.…”

Section: Introductionmentioning

confidence: 99%

Credit default swap pricing with counterparty risk in a reduced form model with a common jump process

Chen

Xing

2022

Prob. Eng. Inf. Sci.

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In this paper, we study the credit default swap (CDS) pricing with counterparty risk in a reduced form model. The default jump intensities of the reference firm and counterparty are both assumed to follow the mean-reverting CIR processes with independent jumps respectively and a common jump. The approximate closed-form solutions of the joint survival probability density and the probability density of the first default can be obtained by using the PDE method. Then with the expressions of the probability densities, we can get the formula for the CDS price with counterparty risk in a reduced form model with a common jump. In the numerical analysis part, we find that the default of the reference asset has a greater impact on the CDS price than that of the default of counterparty after introducing the common jump process.

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Weak Convergence of Path-Dependent SDEs in Basket Credit Default Swap Pricing with Contagion Risk

Cited by 5 publications

References 23 publications

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Basket Credit Default Swap Pricing with Two Defaultable Counterparties

Valuing credit default swaps in uncertain environments

Credit default swap pricing with counterparty risk in a reduced form model with a common jump process

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