tailieunhanh - an introduction to credit risk modeling phần 6

Để phương trình (2 49.) Chúng ta có thể viết biểu thị "sự thật" mặc định xác suất của lớp đánh giá lựa chọn, và có nghĩa là mối tương quan tài sản không rõ của lớp đánh giá xem xét, mà sẽ được ước tính sau đây. P tham số chúng ta không biết chính xác, | 10 FIGURE Asset-Equity relation Equation 3. 20 for parameter sets ỏ r Y ụ- ơa and D 1 - solid 1 - dashed 1 -. dashed-dotted 1 . 2003 CRC Press LLC If we observe E at time t and know the estimate ơE t for the equity volatility then A and ƠA have to solve the equations E D A Ỗ Ỗ A D y ơA D r - HD V r - Hd Y 3. 23 ƠE t ƠAA A oa A ơa Aă ơa -1 3. 24 Y Ỗ r - HdJ As a further simplification it is often assumed that E locally evolves like a geometric Brownian motion which leads to ơE t ƠEE for some ƠE. In the implementation one usually starts with some ƠA ƠA. For example the equity volatility is used to generate two time series As s 0 and Es s 0. Then the volatility of E is estimated and the parameter ƠA is adjusted to a higher or lower level trying to best match the estimated volatility of E with the observed equity volatility. One proceeds that way until the ơE implied by ƠA is close to the observed ƠE. Observe also that the set of equations 3. 23 and 3. 24 can be generalized to any contingent claim approach for the asset values once a functional relationship E E A D ƠA t is specified between assets A debt D and equity E. Conceptually they look like E E A D ơa ƠEE ơaAE A D ơa . This concludes are discussion of asset value models. 2003 CRC Press LLC Chapter 4 The CreditRisk Model In Section we already described the CreditRisk model as a Pois-sonian mixture with gamma-distributed random intensities for each sector. In this section we will explain CreditRisk in some greater detail. The justification for another and more exhaustive chapter on CreditRisk is its broad acceptance by many credit risk managing institutes. Even in the new Capital Accord some references regarding the Basel II approach are Gordy 52 Wilde 126 and the IRB consultative document 103 CreditRisk was originally applied for the calibration of the so-called granularity adjustment in the context of the Internal Ratings-based Approach IRB of .