System for estimating distance-to-default credit risk
A method, computer system, and computer program product are provided for assessing a credit risk of a set of companies. A computer system creates a training data set from distance-to-default values for a first set of companies. The computer system builds a set of predictive models based on the training data set, linking the observed distance-to-default to market capitalization and total liabilities. The computer system forecasts estimated new distance-to-default values for a second set of companies, based on their current distance-to-default (obtained from the Merton approach), and a future change in market capitalization and/or change in total liabilities, according to the set of predictive models.
1. A method comprising:
creating, by a risk estimator of a computer system, a training data set from distance-to-default values for a first set of companies, wherein the risk estimator comprises an artificial intelligence system;
building, by the risk estimator of the computer system, a set of predictive models based on the training data set, wherein the artificial intelligence system comprises the set of predictive models and machine learning of the artificial intelligence system is used to train the set of predictive models using the training data set;
forecasting, by the risk estimator of the computer system, an estimated change in distance-to-default values for a second set of companies according to the set of predictive models; and
assessing, by the risk estimator of the computer system, a credit risk of the second set of companies according to the estimated change in distance-to-default values,
wherein creating the training data set further comprises:
identifying market capitalizations and total liabilities for the first set of companies; and
for each of the first set of companies, determining the distance-to-default values according to the market capitalization and total liabilities of the first set of companies, and
wherein the distance-to-default values for the first set of companies is determined according to:
DD
T
=
ln
(
V
A
D
)
+
(
μ
+
1
2
σ
A
2
)
T
σ
A
T
wherein:
DD T is a distance-to-default at time T;
V A is an asset value;
D is total liabilities;
μ is a mean asset return;
σ A is an asset volatility; and
T is a time horizon,
wherein creating a training data set further comprises:
for each of the first set of companies, generating a set of triplex values from a multiplier ratio, the distance-to-default values for the first set of companies, and modified distance-to-default values for the first set of companies, wherein the training data set comprises the set of triplex values, and
wherein building the set of predictive models further comprises:
separating the set of triplex values into training data subsets, wherein the set of triplex values are separated according to the multiplier ratio and the distance-to-default values of the first set of companies; and
building predictive models based on each of the training data subsets.
2. The method of claim 1 , wherein the estimated change in distance-to-default values for the second set of companies is forecast from the set of predictive models according to market capitalizations and total liabilities of the second set of companies.
3. The method of claim 1 , wherein the asset value V A is determined according to:
V
A
=
V
E
+
Ke
-
rT
*
N
(
d
2
)
N
(
d
1
)
wherein:
V E is an equity value;
N is a cumulative standard normal distribution;
d 1 =DD T ;
d 2 =d 1 −σ A √{square root over (T)};
K is a debt value;
r is a mean asset return; and
T is the time horizon.
4. The method of claim 1 , wherein asset volatility σ A is determined according to:
σ
A
=
(
1
Δ
E
)
*
(
V
E
V
A
)
*
σ
E
wherein:
V E is an equity value;
V A is the asset value;
σ E is an equity volatility; and
Δ E is a measure of a sensitivity of V E to V A .
5. The method of claim 1 , wherein the asset value V A and asset volatility σ A are determined from an iterative solution of a nonlinear system of equations.
6. The method of claim 1 , wherein creating the training data set further comprises:
identifying a set of multipliers for market capitalizations and total liabilities of the first set of companies, wherein each multiplier ratio is a ratio between one of the set of multipliers for the market capitalizations of the first set of companies and one of the set of multipliers for the total liabilities of the first set of companies;
for each of the first set of companies, generating a modified market capitalization and modified total liabilities according to the set of multipliers; and
for each of the first set of companies, determining a set of modified distance-to-default values according to the modified market capitalization and the modified total liabilities.
7. A credit evaluation system comprising:
a computer system; and
a risk estimator in the computer system, wherein the risk estimator operates to:
create a training data set from distance-to-default values for a first set of companies, wherein the risk estimator comprises an artificial intelligence system;
build a set of predictive models based on the training data set, wherein the artificial intelligence system comprises the set of predictive models and machine learning of the artificial intelligence system is used to train the set of predictive models using the training data set;
forecast an estimated change in distance-to-default values for a second set of companies according to the set of predictive models; and
assess a credit risk of the second set of companies according to the estimated change in distance-to-default values,
wherein creating the training data set further comprises:
identifying market capitalizations and total liabilities for the first set of companies; and
for each of the first set of companies, determining the distance-to-default values according to the market capitalization and total liabilities of the first set of companies, and
wherein the distance-to-default values for the first set of companies is determined according to:
DD
T
=
ln
(
V
A
D
)
+
(
μ
+
1
2
σ
A
2
)
T
σ
A
T
wherein:
DD T is a distance-to-default at time T;
V A is an asset value;
D is total liabilities;
μ is a mean asset return;
σ A is an asset volatility; and
T is a time horizon,
wherein creating the training data set further comprises:
for each of the first set of companies, generating a set of triplex values from a multiplier ratio, the distance-to-default values for the first set of companies, and modified distance-to-default values for the first set of companies, wherein the training data set comprises the set of triplex values, and
wherein building the set of predictive models further comprises:
separating the set of triplex values into training data subsets, wherein the set of triplex values are separated according to the multiplier ratio and the distance-to-default values of the first set of companies; and
building predictive models based on each of the training data subsets.
8. The credit evaluation system of claim 7 , wherein the estimated change in distance-to-default values for the second set of companies is forecast from the set of predictive models according to market capitalizations and total liabilities of the second set of companies.
9. The credit evaluation system of claim 7 , wherein the asset value V A is determined according to:
V
A
=
V
E
+
Ke
-
rT
*
N
(
d
2
)
N
(
d
1
)
wherein:
V E is an equity value;
N is a cumulative standard normal distribution;
d 1 =DD T ;
d 2 =d 1 −σ A √{square root over (T)};
K is a debt value;
r is the mean asset return; and
T is the time horizon.
10. The credit evaluation system of claim 7 , wherein asset volatility QA is determined according to:
σ
A
=
(
1
Δ
E
)
*
(
V
E
V
A
)
*
σ
E
wherein:
V E is an equity value;
V A is the asset value;
σ E is an equity volatility; and
Δ E is a measure of a sensitivity of V E to V A .
11. The credit evaluation system of claim 7 , wherein the asset value V A and asset volatility σ A are determined from an iterative solution of a nonlinear system of equations.
12. The credit evaluation system of claim 7 , wherein creating the training data set further comprises:
identifying a set of multipliers for market capitalizations and total liabilities of the first set of companies, wherein each multiplier ratio is a ratio between one of the set of multipliers for the market capitalizations of the first set of companies and one of the set of multipliers for the total liabilities of the first set of companies;
for each of the first set of companies, generating a modified market capitalization and modified total liabilities according to the set of multipliers; and
for each of the first set of companies, determining a set of modified distance-to-default values according to the modified market capitalization and the modified total liabilities.
13. A computer program product comprising:
a non-transitory computer readable storage media;
program code, stored on the computer readable storage media, for creating a training data set from distance-to-default values for a first set of companies, wherein the risk estimator comprises an artificial intelligence system;
program code, stored on the computer readable storage media, for building a set of predictive models based on the training data set, wherein the artificial intelligence system comprises the set of predictive models and machine learning of the artificial intelligence system is used to train the set of predictive models using the training data set; and
program code, stored on the computer readable storage media, for forecasting an estimated change in distance-to-default values for a second set of companies according to the set of predictive models; and
program code, stored on the computer readable storage media, for assessing a credit risk of the second set of companies according to the estimated change in distance-to-default values,
wherein the program code for creating the training data set further comprises:
program code for identifying market capitalizations and total liabilities for the first set of companies; and
program code for determining the distance-to-default values according to the market capitalization and total liabilities of the first set of companies, and
wherein the distance-to-default values for the first set of companies is determined according to:
DD
T
=
ln
(
V
A
D
)
+
(
μ
+
1
2
σ
A
2
)
T
σ
A
T
wherein:
DD T is a distance-to-default at time T;
V A is an asset value;
D is total liabilities;
μ is a mean asset return;
Δ A is an asset volatility; and
T is a time horizon,
wherein creating a training data set further comprises:
program code for generating a set of triplex values from a multiplier ratio, the distance-to-default values for the first set of companies, and modified distance-to-default values for the first set of companies, wherein the training data set comprises the set of triplex values, and
wherein building the set of predictive models further comprises:
program code for separating the set of triplex values into training data subsets, wherein the set of triplex values are separated according to the multiplier ratio and the distance-to-default values of the first set of companies; and
building predictive models based on each of the training data subsets.
14. The computer program product of claim 13 , wherein the estimated change in distance-to-default values for the second set of companies is forecast from the set of predictive models according to market capitalizations and total liabilities of the second set of companies.
15. The computer program product of claim 13 , wherein the asset value V A is determined according to:
V
A
=
V
E
+
Ke
-
rT
*
N
(
d
2
)
N
(
d
1
)
wherein:
V E is an equity value;
N is a cumulative standard normal distribution;
d 1 =DD T ;
d 2 =d 1 −σ A √{square root over (T)};
K is a debt value;
r is the mean asset return; and
T is the time horizon.
16. The computer program product of claim 13 , wherein asset volatility σ A is determined according to:
σ
A
=
(
1
Δ
E
)
*
(
V
E
V
A
)
*
σ
E
wherein:
V E is an equity value;
V A is the asset value;
σ E is an equity volatility; and
Δ E is a measure of a sensitivity of V E to V A .
17. The computer program product of claim 13 , wherein the asset value V A and asset volatility σ A are determined from an iterative solution of a nonlinear system of equations.
18. The computer program product of claim 13 , wherein creating the training data set further comprises:
program code for identifying a set of multipliers for market capitalizations and total liabilities of the first set of companies, wherein each multiplier ratio is a ratio between one of the set of multipliers for the market capitalizations of the first set of companies and one of the set of multipliers for the total liabilities of the first set of companies;
program code for generating a modified market capitalization and modified total liabilities according to the set of multipliers; and
program code for determining a set of modified distance-to-default values according to the modified market capitalization and the modified total liabilities.