Factor Models > 21. Machine learning > Scoring (default probability) assessment

Scoring in credit risk

• Score sn,t:{

indicator of credit-worthinessoutput of a scoring function sn,t = s(zn,t)

• Variables zn,t:

macroeconomicbookmarketprocessed

(see Section 1.4.1)

⇒ the higher the score sn,t, the worse the quality of the obligor

• Bernoulli default indicator:

Xn,t+1|z ≡ 1Dn∈[t,t+1)|z =

{1 with prob. s(z) (if default )0 with prob. 1− s(z) (if no default )

(21.45)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update

Factor Models > 21. Machine learning > Scoring (default probability) assessment

Scoring in credit risk

• Score sn,t:{

indicator of credit-worthinessoutput of a scoring function sn,t = s(zn,t)

• Variables zn,t:

macroeconomicbookmarketprocessed

(see Section 1.4.1)

⇒ the higher the score sn,t, the worse the quality of the obligor

• Bernoulli default indicator:

Xn,t+1|z ≡ 1Dn∈[t,t+1)|z =

{1 with prob. s(z) (if default )0 with prob. 1− s(z) (if no default )

(21.45)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update

Factor Models > 21. Machine learning > Scoring (default probability) assessment

Scoring in credit risk

• Score sn,t:{

indicator of credit-worthinessoutput of a scoring function sn,t = s(zn,t)

• Variables zn,t:

macroeconomicbookmarketprocessed

(see Section 1.4.1)

⇒ the higher the score sn,t, the worse the quality of the obligor

• Bernoulli default indicator:

Xn,t+1|z ≡ 1Dn∈[t,t+1)|z =

{1 with prob. s(z) (if default )0 with prob. 1− s(z) (if no default )

(21.45)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update

Factor Models > 21. Machine learning > Scoring (default probability) assessment

Scoring in credit risk

• Score sn,t:{

indicator of credit-worthinessoutput of a scoring function sn,t = s(zn,t)

• Variables zn,t:

macroeconomicbookmarketprocessed

(see Section 1.4.1)

⇒ the higher the score sn,t, the worse the quality of the obligor

• Bernoulli default indicator:

Xn,t+1|z ≡ 1Dn∈[t,t+1)|z =

{1 with prob. s(z) (if default )0 with prob. 1− s(z) (if no default )

(21.45)

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update

Factor Models > 21. Machine learning > Scoring (default probability) assessment

Tools for scoring assessment

• Receiver Operating Characteristic (ROC) (21.30)

• Area Under Curve (AUC) (21.31)

• Gini index

⇒ probit model (21.8) and logit model (21.7) can be assessed with thesetools

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update

Factor Models > 21. Machine learning > Scoring (default probability) assessment

Tools for scoring assessment

• Receiver Operating Characteristic (ROC) (21.30)

• Area Under Curve (AUC) (21.31)

• Gini index

⇒ probit model (21.8) and logit model (21.7) can be assessed with thesetools

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update

Factor Models > 21. Machine learning > Scoring (default probability) assessment

Credit scoring assessment: logit model and Lorenz curve

• upper plot: Lorenz curve compared to the perfect fit• lower plot: Bernoulli indicator

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update

Factor Models > 21. Machine learning > Scoring (default probability) assessment

Credit scoring assessment: logit model and ROC curve

• upper plot: ROC curve compared to the perfect fit• lower plot: Bernoulli indicator

ARPM - Advanced Risk and Portfolio Management - arpm.co This update: Mar-26-2017 - Last update