rs.calibration {PDtoolkit}

Calibration of the rating scale

Description

rs.calibration performs calibration of the observed default rates for a given rating scale.

Usage

rs.calibration(rs, dr, w, ct, min.pd, method)

Arguments

rs

Rating scale that contain observed default rate and weights used for optimization.

dr

Observed default rate per rating.

w

Weights, usually number of observations (clients/accounts) per rating.

ct

Value of central tendency to which calibration is performed.

min.pd

Minimum probability of default (PD) per rating, as constrain for calibration process.

method

Calibration method. Available options are "scaling", "log.odds.a", "log.odds.ab".

Details

Method "scaling" relies on linear rescaling of observed default rate. Rescaling factor is calculated as a ratio between ct and observed portfolio default rate. Method "log.odds.a" optimize intercept of logit transformation in a way that makes portfolio default rate equal to selected central tendency (ct). Method "log.odds.ab" optimize intercept and slope of logit transformation in a way that makes portfolio default rate equal to selected central tendency (ct). For respecting selected constrain of minimum PD (min.pd), two-stage iterative procedure is implemented. Additional constrain of maximum PD (100%) is also implemented.

Value

The command rs.calibration returns a list of two elements. The first element is vector of calibrated PDs and the second one is dataframe of optimization parameters.

Examples

suppressMessages(library(PDtoolkit))
data(loans)
#estimate some dummy model
mod.frm <- `Creditability` ~ `Account Balance` + `Duration of Credit (month)` +
			`Age (years)`
lr.mod <- glm(mod.frm, family = "binomial", data = loans)
summary(lr.mod)$coefficients
#model predictions
loans$pred <-  unname(predict(lr.mod, type = "response", newdata = loans))
#scale probabilities
loans$score <- scaled.score(probs = loans$pred, score = 600, odd = 50/1, pdo = 20)
#group scores into rating
loans$rating <- sts.bin(x = round(loans$score), y = loans$Creditability, y.type = "bina")[[2]]
#create rating scale
rs <- loans %>%
group_by(rating) %>%
summarise(no = n(),
    nb = sum(Creditability),
    ng = sum(1 - Creditability)) %>%
mutate(dr = nb / no)
rs
#calcualte portfolio default rate
sum(rs$dr * rs$no / sum(rs$no))
#calibrate rating scale to central tendency of 27% with minimum PD of 5%
ct <- 0.33
min.pd <- 0.05
#scaling
pd.calib.s <- rs.calibration(rs = rs, 
			     dr = "dr", 
			     w = "no", 
			     ct = ct, 
			     min.pd = min.pd,
			     method = "scaling")
rs$pd.scaling <- pd.calib.s[[1]]
#log-odds a
pd.calib.a <- rs.calibration(rs = rs, 
			     dr = "dr", 
		 	     w = "no", 
			     ct = ct, 
			     min.pd = min.pd,
			     method = "log.odds.a")
rs$pd.log.a <- pd.calib.a[[1]]
#log-odds ab
pd.calib.ab <- rs.calibration(rs = rs, 
			      dr = "dr", 
		 	      w = "no", 
			      ct = ct, 
			      min.pd = min.pd,
			      method = "log.odds.ab")
rs$pd.log.ab <- pd.calib.ab[[1]]
#checks
rs
sum(rs$pd.scaling * rs$no / sum(rs$no))
sum(rs$pd.log.a * rs$no / sum(rs$no))
sum(rs$pd.log.ab * rs$no / sum(rs$no))