Default Probabilities quantitatively measures the credit risk that a borrower will be unable or unwilling to repay its debt. An accurate model to estimate, as a function of time, these default probabilities is of cruc...Default Probabilities quantitatively measures the credit risk that a borrower will be unable or unwilling to repay its debt. An accurate model to estimate, as a function of time, these default probabilities is of crucial importance in the credit derivatives market. In this work, we adapt Merton’s [1] original works on credit risk, consumption and portfolio rules to model an individual wealth scenario, and apply it to compute this individual default probabilities. Using our model, we also compute the time depending individual default intensities, recovery rates, hazard rate and risk premiums. Hence, as a straight-forward application, our model can be used as novel way to measure the credit risk of individuals.展开更多
The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by ...The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps （CDSs）. Numerical results are presented to show the impacts of the model parameters on the fair spreads.展开更多
We study the smooth-pasting property for a class of conditional expectations with reflected Levy process as underlying state process. A relationship between local times and regulators for the doubly reflected Levy pro...We study the smooth-pasting property for a class of conditional expectations with reflected Levy process as underlying state process. A relationship between local times and regulators for the doubly reflected Levy process is established. As applications, we derive the analytic pricing formula for a zero-coupon defaultable bond when the default intensity （resp. the stochastic loss rate） is modeled as one-sided （resp. double-sided） reflected Levy processes. Finally, some numerical illustrations are provided.展开更多
文摘Default Probabilities quantitatively measures the credit risk that a borrower will be unable or unwilling to repay its debt. An accurate model to estimate, as a function of time, these default probabilities is of crucial importance in the credit derivatives market. In this work, we adapt Merton’s [1] original works on credit risk, consumption and portfolio rules to model an individual wealth scenario, and apply it to compute this individual default probabilities. Using our model, we also compute the time depending individual default intensities, recovery rates, hazard rate and risk premiums. Hence, as a straight-forward application, our model can be used as novel way to measure the credit risk of individuals.
基金Acknowledgements The authors cordially thank the anonymous reviewers for valuable comments to improve the earlier version of the paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371274, 11671291）, the Natural Science Foundation of Jiangsu Province （Grant No. BK20160300）, and the Open Project of Jiangsu Key Laboratory of Financial Engineering （Grant No. NSK2015-05）.
文摘The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps （CDSs）. Numerical results are presented to show the impacts of the model parameters on the fair spreads.
基金supported by National Natural Science Foundation of China(GrantNos.11001213,71201074 and 70932003)NCET-12-0914the Fundamental Research Funds for the Central Universities(Grant No.K5051370001)
文摘We study the smooth-pasting property for a class of conditional expectations with reflected Levy process as underlying state process. A relationship between local times and regulators for the doubly reflected Levy process is established. As applications, we derive the analytic pricing formula for a zero-coupon defaultable bond when the default intensity （resp. the stochastic loss rate） is modeled as one-sided （resp. double-sided） reflected Levy processes. Finally, some numerical illustrations are provided.
