An information processing method executed by an information processing apparatus, the method comprising:
- a z calculating step of calculating via a computing device, based on a confidence level α stored in a storage device, a percentile of a risk factor z corresponding to a using
- z=N−1(1−α);
- a rating threshold calculating step of obtaining via the computing device a probability psk of transition from a rating s to a rating k stored in the storage device, and
- calculating via the computing device 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 step of obtaining a constant ai of each obligor stored in the storage device, and calculating via the computing device 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 step, and the θir calculated in the rating threshold calculating step using
- ps
- ir
-
- (
- z
- )
- =
- N
-
- (
- θ
- ir
- -
- a
- i
-
- z
- 1
- -
- a
- i
- )
- where N is a cumulative probability function of a standard normal distribution;
- a wir calculating step of calculating via the computing device 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 step of calculating, via the computing device, a conditional expected value 1(z) of a portfolio value V under a condition that z is fixed based on wir calculated in the wir calculating step and psir(z) calculated in the conditional probability calculating step using
- l
- i
-
- (
- z
- )
- =
- ∑
- r
-
- w
- ir
-
- p
-
-
- s
- ir
-
- (
- z
- )
- l
-
- (
- z
- )
- =
- E
-
- [
- V
- |
- z
- ]
- =
- ∑
- i
-
- l
- i
-
- (
- z
- )
- ;
- a conditional variance calculating step of calculating, via the computing device, a conditional variance v(z) of the portfolio value V under a condition that z is fixed based on wir calculated in the wir calculating step and psir(z) calculated in the conditional probability calculating step using
- v
- i
-
- (
- z
- )
- =
- V
- i
-
- ∂
- ∂
- V
- i
-
- Var
-
- [
- V
- |
- z
- ]
- v
-
- (
- z
- )
- =
- 1
- 2
-
- ∑
- i
-
- v
- i
-
- (
- z
- )
- ;
- a qα calculating step of calculating, via the computing device, a percentile qα of a portfolio value based on a first derivative 1′(z) of 1(z) calculated in the conditional expected value calculating step, a second derivative 1″(z) of 1(z) calculated in the conditional expected value calculating step, v(z) calculated in the conditional variance calculating step, and a first derivative v′(z) of v(z) calculated in the conditional variance calculating step 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
- ;
- an E[Vi] calculating step of obtaining, via the computing device, 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 step of calculating, via the computing device, a portfolio VaR from the percentile qαi and the expected value E[Vi] of the exposure value of the obligor I,
- wherein the rating threshold calculating unit includes:
- a pssr calculating step of calculating, via the computing device, 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 step of obtaining, via the computing device, a probability psi, of transition of the obligor i to the rating r or lower based on the probability pssr calculated in the pssr calculating step;
- and
- a θir calculating step of calculating, via the computing device, 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 step using θir=N−1(psir).