On Portfolio’s Default-Risk-Adjusted Duration and Value: Model and Algorithm Based on Copulas
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In this paper, we propose a new approach, copulas, to calculating the default-risk-adjusted duration and present value for a portfolio of bonds vulnerable to default risk. A copula function is used to determine the default dependence structure and simulate correlated default time from individual obligor’s default distribution. This approach is verified to be effective and applicable by a numerical example, in which we demonstrate how to calculate the default-risk-adjusted duration and present value for a given portfolio. In the process we take into account of the settlement time when default happens, the choice of copula function and the correlation between obligors, and make a sensitive analysis of the influence of Kendall’s tau and copula functions on the default-risk-adjusted duration and present value. Results show that the duration and present value simulated from Gaussian copula fluctuates larger than that from Clayton and Gumbel copulas when Kendall’s tau varies from zero to one.
KeywordsCredit Default Swap Default Risk Default Probability Credit Spread Copula Function
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