Credit survival, probability

The probability of survival for a credit may be viewed as a decreasing function against time. The survival probabilities for each traded reference credit can be derived from it s credit curve. The survival probability is a decreasing function because it reflects the fact that the probability of survival for a credit reduces over time. For example, the probability of survival to year 3 is higher than the probability of survival to year 5. 

Under nonvolatile market conditions, the shape of the survival probability and the resulting credit curve will take a different form to the shape implied in volatile market conditions the graphs may change to reflect the higher perceived likelihood of default. For example, the shape of the survival probability may take the form as shown in Exhibit 21.19. 

The corresponding credit curves, which are consistent with these survival probabilities, take the form shown in Exhibit 21.20. This shows that the credit curve inversion is consistent with the changes in the survival probability functions. 

Take for example an issuer s new five-year bond that just hit the market today. This bond pays a 5.00% annual coupon and returns its entire principal amount at maturity. Since each of the five annual cash flows of the bond are subject to the issuer s credit risk they must be multiplied by their respective survival probabilities and discount factors or more exactly e ... 

The NX CR Engine is a pricing and risk management tool that allows users to model a wide range of credit derivative products. It produces theoretical prices for single-name credit default swaps, baskets and CDOs. In addition, NumeriX s software produces survival probabilities, recovery rates and correlations. 

The worst case reliability function [Bishop 2002a] has similar in shape to the Bayesian reliability function where the probability of operating without failure R(dr) decreases almost inversely with the number of tests t. We have two ways of using the worst case theory —using the initial value of N-6 and 7=2.2 10 or the final fractional value of iV. 26, but claim no credit for prior testing (7=0). As mentioned earlier, when the number of residual faults N is fractional, the probability of survival is asymptotic to l-N for the case where AH).26, the asymptote is 74%. The reliability predictions are shown Figure 9. 

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