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an introduction to credit risk modeling phần 7

nhưng sau khi suy nghĩ của một thời điểm, nó sẽ được rõ ràng rằng có ý nghĩa lịch sử quan sát thấy tần số mặc định p cho chúng ta một proxy tốt đẹp của tỷ lệ mặc định có nghĩa là "true". Chỉ cần lưu ý rằng nếu Lưu ý Trước khi kết thúc phần này chúng tôi một thời gian ngắn đề cập đến | 5.2.2 Capital Allocation w.r.t. Value-at-Risk Calculating risk contributions associated with the VaR risk measure is a natural but difficult attempt since in general the quantile function will not be differentiable with respect to the asset weights. Under certain continuity assumptions on the joint density function of the random variables Xi differentiation of VaRa X where X Cị WịXi is guaranteed. One has see 122 dVaR X E Xi I X VaRa X . 5. 1 Unfortunately the distribution of the portfolio loss L WjLi as specified at the beginning of this chapter is purely discontinuous. Therefore the derivatives of VaRa in the above sense will either not exist or vanish to zero. In this case we could still define risk contributions via the right-hand-side of Equation 5. 1 by writing Yi E Li I L VaRa L - E Li . 5. 2 For a clearer understanding note that dE L E L i and V WiYi ECvaRa dwi Additionally observe that for a large portfolio and on an appropriate scale the distribution of L will appear to be close to continuous . Unfortunately even in such approximately good cases the loss distribution often is not given in an analytical form in order to allow for differentiations. Remark For the CreditRisk model an analytical form of the loss distribution can be found see Section 2.4.2 and Chapter 4 for a discussion of CreditRisk . Tasche 121 showed that in the CreditRisk framework the VaR contributions can be determined by calculating the corresponding loss distributions several times with different parameters. Martin et al. 82 suggested an approximation to the partial derivatives of VaR via the so-called saddle point method. Capital allocation based on VaR is not really satisfying because in general although RCi i i . TO might be a reasonable partition of the portfolio s standard deviation it does not really say much about the 2003 CRC Press LLC tail risks captured by the quantile on which VaR-EC is relying. Even if in general one views capital allocation by means of partial derivatives