US 2010/0306131 A1 · INFORMATION PROCESSING APPARATUS, INFORMATION PROCESSING METHOD, AND PROGRAM PRODUCT

Abstract

An information processing apparatus includes: a rating threshold calculating unit obtaining a probability psk of transition from a rating s to a rating k stored in the storage device, and calculating a rating threshold θir at which the rating of a obligor i becomes a rating r or lower based on the obtained psk, a conditional probability calculating unit obtaining a constant ai of each obligor i stored in the storage device, and calculating a probability psir(z) that the rating of the obligor i becomes the rating r or lower under a condition that z is fixed based on the obtained ai, z calculated in the z calculating unit, and the θir calculated in the rating threshold calculating unit, and a wir calculating unit calculating a difference Wir in exposure value between adjacent ratings of the obligor i based on an exposure value Vir of the obligor i when transition from a current rating to the rating r occurs, which is stored in the storage device.

Claims13

Dependent claims

An information processing apparatus, comprising:

a z calculating unit calculating, based on a confidence level a stored in a storage device, a percentile of a risk factor z corresponding to a;
a rating threshold calculating unit obtaining a probability psk of transition from a rating s to a rating k stored in the storage device, and calculating a rating threshold θir at which the rating of a obligor i. becomes a rating r or lower based on the obtained psk;
a conditional probability calculating unit obtaining a constant ai of each obligor i stored in the storage device, and calculating a probability psir(z) that the rating of the obligor i becomes the rating r or lower under a condition that z is fixed based on the obtained ai, z calculated in the z calculating unit, and the θir calculated in the rating threshold calculating unit using
p


s
ir

(
z
)
=
N

(
θ
ir

-
a
i

z
1
-
a
i
)
[
Expression


1
]
where N is a cumulative probability function of a standard normal distribution;
and
a wir calculating unit calculating a difference wir in exposure value between adjacent ratings of the obligor i based on an exposure value Vir of the obligor i when transition from a current rating to the rating r occurs, which is stored in the storage device, using wir=Vir−Vi(r+1).

35 more elements

An information processing apparatus, comprising:

a z calculating unit calculating, based on a confidence level α stored in a storage device, a percentile of a risk factor z corresponding to α using z=N−1(1−α);
a rating threshold calculating unit obtaining a probability psk of transition from a rating s to a rating k stored in the storage device, and calculating a rating threshold θir at which the rating of a obligor i becomes a rating r or lower based on the obtained psk;
a conditional probability calculating unit obtaining a constant ai of each obligor i stored in the storage device, and calculating a probability psir(z) that the rating of the obligor i becomes the rating r or lower under a condition that z is fixed based on the obtained ai, z calculated in the z calculating unit, and the θir calculated in the rating threshold calculating unit using
p


s
ir

(
z
)
=
N

(
θ
ir
-
a
i

z
1
-
a
i
)
[
Expression


7
]
where N is a cumulative probability function of a standard normal distribution;
a wir calculating unit calculating a difference wir in exposure value between adjacent ratings of the obligor i based on an exposure value Vir of the obligor i when transition from a current rating to the rating r occurs, which is stored in the storage device, using wir=Vir−Vi(r+1);
a conditional expected value calculating unit calculating a conditional expected value l(z) of a portfolio value V under a condition that z is fixed based on wir calculated in the wir calculating unit and psir(z) calculated in the conditional probability calculating unit using
l
i

(
z
)
=
∑
r

w
ir

p


s
ir

(
z
)


l

(
z
)
=
E

[
V
|
z
]
=
∑
i

l
i

(
z
)
;
[
Expression


8
]
a conditional variance calculating unit calculating a conditional variance ν(z) of the portfolio value V under a condition that z is fixed based on wir calculated in the wir calculating unit and psir(z) calculated in the conditional probability calculating unit using
v
i

(
z
)
=
V
i

∂
∂
V
i

Var
[
V
|
z
]
[
Expression


9
]
v

(
z
)
=
1
2

∑
i

v
i

(
z
)
;
a qα calculating unit calculating a percentile qα of a portfolio value based on a first derivative l′(z) of l(z) calculated in the conditional expected value calculating unit, a second derivative l″(z) of l(z) calculated in the conditional expected value calculating unit, ν(z) calculated in the conditional variance calculating unit, and a first derivative ν′(z) of ν(z) calculated in the conditional variance calculating unit using
Δ


q
α


i

(
z
)
=
V
i

∂
∂
V
i

{
-
1
2

l
′

(
z
)

(
v
′

(
z
)
-
v

(
z
)
(
l
″

(
z
)
l
′

(
z
)
+
z
)
)
}


Δ


q
α

(
z
)
=
∑
i

Δ


q
α


i


q
α


i
=
(
l
i

(
z
)
+
Δ


q
α


i

(
z
)
)

|
z
=
N
-
1

(
1
-
α
)


q
α
=
∑
i

q
α


i
;
[
Expression


10
]
an E[Vi] calculating unit obtaining an exposure value Vir of the obligor i when transition from a current rating to the rating r occurs, which is stored in the storage device, and obtaining a probability pir of transition from a rating i to the rating r stored in the storage device, and calculating an expected value E[Vi] of an exposure value of the obligor i based on the obtained Vir and probability pir using
E

[
V
i
]
=
∑
r

p
ir

V
ir
;
and
a portfolio VaR calculating unit calculating a portfolio VaR based on E[Vi] calculated in the E[Vi] calculating unit and qα calculated in the qα calculating unit using
Portfolio


VaR
=
q


α
-
∑
i

E
[
V
i
]
,
wherein the rating threshold calculating unit includes:
a pssr calculating unit calculating a probability pssr of transition from the rating s to the rating r or lower based on the probability psk using
p


s
sr
=
∑
k
=
1
r

p
sk
;
a psir calculating unit obtaining a probability psir of transition of the obligor i to the rating r or lower based on the probability pssr calculated in the pssr calculating unit;
and
a θir calculating unit calculating the rating threshold θir at which the rating of the obligor i becomes the rating r or lower based on the probability psir obtained in the psir calculating unit using θir=N−1(psir).

343 more elements

An information processing apparatus, comprising:

a z calculating unit calculating, based on a confidence level α stored in a storage device, a percentile of a risk factor z corresponding to α using z=N−1(1−α);
a rating threshold calculating unit obtaining a probability psk of transition from a rating s to a rating k stored in the storage device, and calculating a rating threshold θir at which the rating of a obligor i becomes a rating r or lower based on the obtained psk;
a conditional probability calculating unit obtaining a constant ai of each obligor i stored in the storage device, and calculating a probability psir(z) that the rating of the obligor i becomes the rating r or lower under a condition that z is fixed based on the obtained ai, z calculated in the z calculating unit, and the θir calculated in the rating threshold calculating unit using
p


s
ir


(
z
)
=
N

(
θ
ir
-
a
i

z
1
-
a
i
)
[
Expression


11
]
where N is a cumulative probability function of a standard normal distribution;
a wir calculating unit calculating a difference wir in exposure value between adjacent ratings of the obligor i based on an exposure value Vir of the obligor i when transition from a current rating to the rating r occurs, which is stored in the storage device, using wir=Vir−Vi(r+1);
a conditional expected value calculating unit calculating a conditional expected value l(z) of a portfolio value V under a condition that z is fixed based on wir calculated in the wir calculating unit and psir(z) calculated in the conditional probability calculating unit using
l
i

(
z
)
=
∑
r

w
ir

p


s
ir

(
z
)


l

(
z
)
=
E

[
V
|
z
]
=
∑
i

l
i

(
z
)
;
[
Expression


12
]
a conditional variance calculating unit calculating a conditional variance ν(z) of the portfolio value V under a condition that z is fixed based on wir calculated in the wir calculating unit and psir(z) calculated in the conditional probability calculating unit using
v
i

(
z
)
=
V
i

∂
∂
V
i

Var
[
V
|
z
]


v

(
z
)
=
1
2

∑
i

v
i

(
z
)
;
[
Expression


13
]
a qα calculating unit calculating a percentile qα of a portfolio value based on a first derivative l′(z) of l(z) calculated in the conditional expected value calculating unit, a second derivative l″(z) of l(z) calculated in the conditional expected value calculating unit, ν(z) calculated in the conditional variance calculating unit, and a first derivative ν′(z) of ν(z) calculated in the conditional variance calculating unit using
Δ


q
α


i

(
z
)
=
V
i

∂
∂
V
i

{
-
1
2

l
′

(
z
)

(
v
′

(
z
)
-
v

(
z
)
(
l
″

(
z
)
l
′

(
z
)
+
z
)
)
}


Δ


q
α

(
z
)
=
∑
i

Δ


q
α


i


q
α


i
=
(
l
i

(
z
)
+
Δ


q
α


i

(
z
)
)

|
z
=
N
-
1

(
1
-
α
)


q
α
=
∑
i

q
α


i
;
[
Expression


14
]
an E[Vi] calculating unit obtaining an exposure value Vir of the obligor i when transition from a current rating to the rating r occurs, which is stored in the storage device, and obtaining a probability pir of transition from a rating i to the rating r stored in the storage device, and
calculating an expected value E[Vi] of an exposure value of the obligor i based on the obtained Vir and probability pir as
E

[
V
i
]
=
∑
r

p
ir


V
ir
;
and
a risk contribution calculating unit calculating a risk contribution of a obligor i based on E[Vi] calculated in the E[Vi] calculating unit and qαi calculated when calculating qα in the qα calculating unit using
risk contribution of a obligor i=qαi−E[Vi],
wherein the rating threshold calculating unit includes:
a pssr calculating unit calculating a probability pssr of transition from the rating s to the rating r or lower based on the probability psk using
p


s
sr
=
∑
k
=
1
r

p
sk
;
a psir calculating unit obtaining a probability psir of transition of the obligor i to the rating r or lower based on the probability pssr calculated in the pssr calculating unit;
and
a θir calculating unit calculating the rating threshold θir at which the rating of the obligor i becomes the rating r or lower based on the probability psir obtained in the psir calculating unit using θir=N−1(psir).

330 more elements

Dependencies are inferred from the claim text.

Information processing apparatus, information processing method, and program product

Life of this patent

Information processing apparatus, information processing method, and program product

Life of this patent

Abstract

Claims13