Volume 12, Issue 5
Valuation of Basket Credit Default Swaps Under Stochastic Default Intensity Models

Adv. Appl. Math. Mech., 12 (2020), pp. 1301-1326.

Published online: 2020-07

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• Abstract

Portfolio credit derivatives, including the basket credit default swaps, are designed to facilitate the transfer of credit risk amongst market participants. Investors consider them as cheap tools to hedge a portfolio of credits, instead of individual hedging of the credits. The prime aim of this work is to model the hazard rate process using stochastic default intensity models, as well as extend the results to the pricing of basket default swaps. We focused on the  $n$th-to-default swaps whereby the spreads are dependent on the $n$th default time, and we estimated the joint survival probability distribution functions of the intensity models under the risk-neutral pricing measure, for both the homogeneous and the heterogeneous portfolio. This work further employed the Monte-Carlo method, under the one-factor Gaussian copula model to numerically approximate the distribution function of the default time, and thus, the numerical experiments for pricing the $n$th default swaps were made viable under the two portfolio types. Finally, we compared the effects of different swap parameters to various $n$th-to-default swaps.

• Keywords

Portfolio credit derivatives, basket default swaps, Gaussian copula, Monte-Carlo simulations, stochastic intensity modelling, hazard rate, joint survival probability distribution.

91G20, 91G30, 91G40, 91G60, 91G70, 62P05, 65C05

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• RIS
• TXT
@Article{AAMM-12-1301, author = {Nneka Umeorah , and Matthias Ehrhardt , and Phillip Mashele , }, title = {Valuation of Basket Credit Default Swaps Under Stochastic Default Intensity Models}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {5}, pages = {1301--1326}, abstract = {

Portfolio credit derivatives, including the basket credit default swaps, are designed to facilitate the transfer of credit risk amongst market participants. Investors consider them as cheap tools to hedge a portfolio of credits, instead of individual hedging of the credits. The prime aim of this work is to model the hazard rate process using stochastic default intensity models, as well as extend the results to the pricing of basket default swaps. We focused on the  $n$th-to-default swaps whereby the spreads are dependent on the $n$th default time, and we estimated the joint survival probability distribution functions of the intensity models under the risk-neutral pricing measure, for both the homogeneous and the heterogeneous portfolio. This work further employed the Monte-Carlo method, under the one-factor Gaussian copula model to numerically approximate the distribution function of the default time, and thus, the numerical experiments for pricing the $n$th default swaps were made viable under the two portfolio types. Finally, we compared the effects of different swap parameters to various $n$th-to-default swaps.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0141}, url = {http://global-sci.org/intro/article_detail/aamm/17750.html} }
TY - JOUR T1 - Valuation of Basket Credit Default Swaps Under Stochastic Default Intensity Models AU - Nneka Umeorah , AU - Matthias Ehrhardt , AU - Phillip Mashele , JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1301 EP - 1326 PY - 2020 DA - 2020/07 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0141 UR - https://global-sci.org/intro/article_detail/aamm/17750.html KW - Portfolio credit derivatives, basket default swaps, Gaussian copula, Monte-Carlo simulations, stochastic intensity modelling, hazard rate, joint survival probability distribution. AB -

Portfolio credit derivatives, including the basket credit default swaps, are designed to facilitate the transfer of credit risk amongst market participants. Investors consider them as cheap tools to hedge a portfolio of credits, instead of individual hedging of the credits. The prime aim of this work is to model the hazard rate process using stochastic default intensity models, as well as extend the results to the pricing of basket default swaps. We focused on the  $n$th-to-default swaps whereby the spreads are dependent on the $n$th default time, and we estimated the joint survival probability distribution functions of the intensity models under the risk-neutral pricing measure, for both the homogeneous and the heterogeneous portfolio. This work further employed the Monte-Carlo method, under the one-factor Gaussian copula model to numerically approximate the distribution function of the default time, and thus, the numerical experiments for pricing the $n$th default swaps were made viable under the two portfolio types. Finally, we compared the effects of different swap parameters to various $n$th-to-default swaps.

Nneka Umeorah, Matthias Ehrhardt & Phillip Mashele. (2020). Valuation of Basket Credit Default Swaps Under Stochastic Default Intensity Models. Advances in Applied Mathematics and Mechanics. 12 (5). 1301-1326. doi:10.4208/aamm.OA-2019-0141
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