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The credit spread sensitivity is defined as the change in the MTM by perturbing the credit spread by a small amount; the default sensitivity is calculated by assuming that one obligor in the collateral pool defaults right away; and the correlation sensitivity is computed by perturbing the index base correlations by a small amount.
https://ia601405.us.archive.org/35/items/dailyDigital/dailyDigital.pdf
Risk Measures for Index Tranches and Bespoke CDOs
Risk Measures for Index Tranches and Bespoke CDOs
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