Benchmarking Deutsche Bundesbank's Default Risk Model, the KMV 

renef

Downloading requires you to have access to the YouScribe library
Learn all about the services we offer

About
Information

Description

exposé - matière potentielle : 2 years of fin
exposé - matière potentielle : plus market trend information
exposé
exposé - matière potentielle : information
fiche de synthèse - matière potentielle : the model dimensions

- 1 - Benchmarking Deutsche Bundesbank's Default Risk Model, the KMV Private Firm Model and Common Financial Ratios for German Corporations Stefan Blochwitz1 Thilo Liebig1 Mikael Nyberg Deutsche Bundesbank Deutsche Bundesbank KMV, LLC November 2000 Abstract: By comparing Gini curves and Gini coefficients that are determined on the same underlying dataset, we assess the discriminative power of Deutsche Bundesbank's Default Risk Model, KMV's Private Firm Model and common financial ratios for German corporations.

discriminative power
credit score
random gini curve
deutsche bundesbank
quantitative properties for further analysis
rating methodology
probabilities of default
minimum
model

Subjects

Documents

Education

Quizzes and revision

Exposé

Information

Private sector

Corporation

Informations

Published by	renef
Reads	26
Language	English

From the same publisher

HSC Physics Summary

Stophs2 consultation July11 Final

Letts GCSE Success Revision Guides

Introduction to Ionospheric Physics

Does Good Corporate Governance Include Employee Representation ...

1 (37th Session) NATIONAL ASSEMBLY SECRETARIAT ...

MA441: Algebraic Structures I
Lecture 2
8 September 2003
1Review:
A group G is a set with a binary operation that
satisﬁes four properties:
Closure
Associativity
Identity
Inverses
2Note:
The associativity property lets us write a com-
position without parentheses:
abc= a(bc)=(ab)c.
nFor a positive integer n, we write a for the
product of a taken n times.
1 nWhen n is negative, we mean (a ) .
0We take a = e.
3(From Chapter 0, page 5)
Division Algorithm
Leta,bbeintegerswithb >0. Thenthereexist
unique integers q,r with the property that
a= qb+r,
where 0 r < b.
Example:
Let a = 17 and b = 5. Then a = 3b + 2
(q =3,r =2).
4Deﬁnition:
Thegreatestcommondivisoroftwononzero
integers a and b is the largest of all common
divisors of a and b. We denote this integer by
gcd(a,b).
When gcd(a,b) = 1, we say that a and b are
relatively prime.
Fact: GCD is a linear combination
For any nonzero integers a,b, there exist in-
tegers s and t such that gcd(a,b) = as+ bt.
Moreover, gcd(a,b) is the smallest positive in-
teger of the form as+bt.
5By repeatedly applying the division algorithm
to two nonzero integers a and b, we can com-
pute gcd(a,b) and the linear combination
gcd(a,b)= as+bt.
Example:
a=17,b=5
17 = 35+2
5 = 22+1.
We can work backwards to write
1 = 5 22
2 = 17 35
1 = 5 2(17 35)
= 75 217.
6Note:
Let a,b be two relatively prime integers.
We can ﬁnd s,t such that as+bt=1.
Then as 1 (mod b) and we say that a has a
multiplicative inverse modulo b.
Likewise, bt1 (mod a) and we say that b has
a multiplicative inverse modulo a.
7(From Chapter 1, page 33)
Deﬁnition:
Let G be a group of n elements.
ACayleytable(oroperationtable)isatable
with n rows, indexed by the elements of G,
and n columns, also indexed by G, such that
the table entry corresponding to (a,b) is the
product (or composition) ab in G.
Example
The dihedral group of an equilateral triangle,
D , has 6 elements corresponding to rotation3
by0,120,and240degreesandreﬂectionabout
an axis going through each vertex.
8(Chapter 2, page 49)
Deﬁnition:
Let S be a subset of a group G. We say that
S generates G if every element of G can be
written as a product of elements of S or their
inverses.
In other words, for any g in G, there are xi
1(i = 1...n) such that either x or x is in Si i
and
g = x x x .n1 2
We say that S is a set of generators for G.
9Example:
The dihedral group D is generated by a rota-4
tion and a ﬂip. For example, let R = R and90
F = V be the ﬂip about the vertical axis.
2 3 4Compute R,R ,R ,R = e. Then apply F to
2 3these four elements to get RF,R F,R F,F.
10