tailieunhanh - an introduction to credit risk modeling phần 2

bắt đầu một nghề nghiệp như quản lý rủi ro danh mục đầu tư để có được truy cập nhanh vào thế giới của quản lý rủi ro tín dụng. Thứ hai, cuốn sách của chúng tôi là nhằm mục đích hữu ích để quản lý rủi ro đang tìm kiếm một cách tiếp cận định lượng rủi ro tín dụng. | of the underlying portfolio. The empirical distribution function can be determined as follows 1 n vưo niWO QỈ mill atorl T rAiOtontiol TOíOrtTíolỉíO liOQQOQ ssume we ave simulate n poten a por o o osses pf pF hereby taking the driving distributions of the single loss variables and their correlations12 into account. Then the empirical loss distribution function is given by F x l 0 x LpF n j 1 1. 12 Figure shows the shape of the density histogram of the randomly nnmhprR rr n L. i íõf tì ìõ prrrnìrìcRl íõf generate num ers PF PF o e emprca oss str u on oi some test portfolio. From the empirical loss distribution we can derive all the portfolio risk quantities introduced in the previous paragraphs. For example the a-quantile of the loss distribution can directly be obtained from .111. I Hl 111 1 I n H Ii iill Í rf l r III .li 1 ill our simulation results LpF LpF as iollows . Starting with order statistics of LpF LpF say fl i11 r fl if r r fl in LpF LPF l pf the a-quantile qa of the empirical loss distribution for any confidence level a is given by qa r i I 1 r .z na 1 if aLpF 1 a LpF if . .i. if na G N na ị N 1. 13 where na min k G 1 n na k The economic capital can then be estimated by 1n ECa qa n Lpf E 14 In an analogous manner any other risk quantity can be obtained by calculating the corresponding empirical statistics. 12 We will later see that correlations are incorporated by means of a factor model. 2003 CRC Press LLC FIGURE An empirical portfolio loss distribution obtained by Monte Carlo simulation. The histogram is based on a portfolio of middle-size corporate loans. 2003 CRC Press LLC Approaching the loss distribution of a large portfolio by Monte Carlo simulation always requires a sound factor model see Section . The classical statistical reason for the existence of factor models is the wish to explain the variance of a variable in terms of underlying factors. Despite the fact that in credit risk we also wish to