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9 records were found.

Credit default,credit derivative,default dependence,structural form models,threshold model
We investigate the problem of modeling defaults of dependent credits. In the framework of the class of structural default models we study threshold models where for each credit the underling ability-to-pay process is a transformation of a Wiener processes. We propose a model for dependent defaults based on correlated Wiener processes whose time scales are suitably transformed in order to calibrate the model to given marginal default distributions for each underlying credit. At the same time the model allows for a straightforward analytic calibration to dependency information in the form of joint default probabilities.
This paper provides a general framework for doubly stochastic term structure models for portfolio of credits, such as collateralized debt obligations (CDOs). We introduce the defaultable (T, x)-bonds, which pay one if the aggregated loss process in the underlying pool of the CDO has not exceeded x at maturity T, and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Moreover, we show that any exogenous specification of the forward rates and spreads volatility curve actually yields a consistent loss process and thus an arbitrage-free family of (T, x)-bond prices. For the sake of analytical and computational efficiency we then develop a tractable class of affine term structure models.
This paper provides a unifying approach for valuing contingent claims on a portfolio of credits, such as collateralized debt obligations (CDOs). We introduce the defaultable (T, x)-bonds, which pay one if the aggregated loss process in the underlying pool of the CDO has not exceeded x at maturity T, and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Background market risk as well as feedback contagion effects of the loss process are taken into account. Moreover, we show that any exogenous specification of the volatility and contagion parameters actually yields a unique consistent loss process and thus an arbitrage-free family of (T, x)-bond prices. For the sake of analytical and computational efficiency we then develop a tractable class of doubly stochas...
We investigate default probabilities and default correlations of Merton-type credit portfolio models in stress scenarios where a common risk factor is truncated. The analysis is performed in the class of elliptical distributions, a family of light-tailed to heavy-tailed distributions encompassing many distributions commonly found in financial modelling. It turns out that the asymptotic limit of default probabilities and default correlations depend on the max-domain of the elliptical distribution's mixing variable. In case the mixing variable is regularly varying, default probabilities are strictly smaller than 1 and default correlations are in (0; 1). Both can be expressed in terms of the Student t-distribution function. In the rapidly varying case, default probabilities are 1 and default correlations are 0. We compare our results to t...
Values of tranche spreads of collateralized debt obligations (CDOs) are driven by the joint default performance of the assets in the collateral pool. The dependence between the names in the portfolio mainly depends on current economic conditions. Therefore, a correlation implied from tranches can be seen as a measure of the general health of the credit market. We analyse the European market of standardized CDOs using tranches of iTraxx index in the periods before and during the global financial crisis. We investigate the evolution of the correlations using different copula models: the standard Gaussian, the NIG, the double-t, and the Gumbel copula model. After calibration of these models one obtains a time varying vector of parameters. We analyse the dynamic pattern of these coefficients. That enables us to forecast future parameters a...
Values of tranche spreads of collateralized debt obligations (CDOs) are driven by the joint default performance of the assets in the collateral pool. The dependence between the names in the portfolio mainly depends on current economic conditions. Therefore, a correlation implied from tranches can be seen as a measure of the general health of the credit market. We analyse the European market of standardized CDOs using tranches of iTraxx index in the periods before and during the global financial crisis. We investigate the evolution of the correlations using different copula models: the standard Gaussian, the NIG, the double-t, and the Gumbel copula model. After calibration of these models one obtains a time varying vector of parameters. We analyse the dynamic pattern of these coefficients. That enables us to forecast future parameters a...
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