By C.Bluhm, L.Overbeck & C.Wagner
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Additional resources for An Introduction to Credit Risk Modeling
10), Corr[Li , Lj ] = 1, implies a “rigid” behaviour of single losses in the portfolio: Either all counterparties default or all counterparties survive simultaneously. The corresponding distribution F of P is then a Bernoulli distribution, such that P = 1 with probability p and P = 0 with probability 1 − p. This means that sometimes (such events occur with probability p), all counterparties default and the total portfolio exposure is lost. In other scenarios (occurring with probability 1 − p), all obligors survive and not even one dollar is lost.
28) (i) where ci is the threshold corresponding to Ci after exchanging AT by ri . Applying (2. , m). (2. 29) Now, in both models, the standard valuation horizon is T = 1 year. Denoting the one-year default probability of obligor i by pi , we naturally have pi = P[ri < ci ]. , m), (2. 30) 11 Shifted and scaled in order to obtain a random variable with mean zero and standard deviation one. 3, where we wrote r˜i . ©2003 CRC Press LLC where N [·] denotes the cumulative standard normal distribution function.
In the documentation of the so-called Internal Ratings-Based Approach (IRB) , the only quantity reflecting the portfolio as a whole is the granularity adjustment, which is still in discussion and likely to be removed from the capital accord. In particular, industrial or regional diversification effects are not reflected by regulatory capital if the new Basel Accord in its final form, which will be negotiated in the near future, keeps the approach documented in . So in order to better capture the risk models widely applied in banks all over the world, some further evolution of the Basel process is necessary.
An Introduction to Credit Risk Modeling by C.Bluhm, L.Overbeck & C.Wagner