heterogeneity {LGDtoolkit}

Testing heterogeneity of the LGD rating model

Description

heterogeneity performs heterogeneity testing of LGD model based on the rating pools. This test is usually applied on application portfolio, but it can be applied also on model development sample.

Usage

heterogeneity(app.port, loss, pools, method = "t.test", alpha = 0.05)

Arguments

app.port

Application portfolio (data frame) which contains realized loss (LGD) values and LGD pools in use.

loss

Name of the column that represents realized loss (LGD).

pools

Name of the column that represents LGD pools.

method

Statistical test. Available options are t.test (default) and wilcox.test.

alpha

Significance level of statistical test. Default is 0.05.

Details

Testing procedure starts with summarizing the number of observations and average loss per LGD pool. After that statistical test is applied on adjacent rating grades. Testing hypothesis is that average realized loss of pool i is less or greater than average realized loss of pools i - 1, where i takes the values from 2 to the number of unique pools. Direction of alternative hypothesis (less or greater) is determined automatically based on correlation direction of realized average loss per pool. Incomplete cases, identified based on realized loss (loss) and rating pool (pools) columns are excluded from the summary table and testing procedure. If identified, warning will be returned.

Value

The command heterogeneity returns a data frame with the following columns:

• pool: Unique values of pool from application portfolio.

• no: Number of complete observations.

• mean: Average realized loss.

• alpha: Selected significance level

• p.val: Test p-value.

• res: Accepted hypothesis.

Examples

library(monobin)
library(LGDtoolkit)
data(lgd.ds.c)
#build dummy model
rf <- c("rf_02", "rf_01", "rf_16", "rf_03", "rf_09")
for   (i in 1:length(rf)) {
     rf_l <- rf[i]
     lgd.ds.c[, rf_l] <- sts.bin(x = lgd.ds.c[, rf_l], 
                                 y = lgd.ds.c[, "lgd"])[[2]]	
     }
str(lgd.ds.c)
frm <- paste0("lgd ~ ", paste(rf, collapse = " + "))
model <- lm(formula = as.formula(frm), data = lgd.ds.c)
summary(model)$coefficients
summary(model)$r.squared
#create lgd pools
lgd.ds.c$pred <- unname(predict(model))
lgd.ds.c$pool <- sts.bin(x = lgd.ds.c$pred, 
                        y = lgd.ds.c$lgd)[[2]]
#create dummy application portfolio
set.seed(642)
app.port <- lgd.ds.c[sample(1:nrow(lgd.ds.c), 500, replace = FALSE), ]
#simulate realized lgd values
app.port$lgd.r <- app.port$lgd
#test heterogeneity
heterogeneity(app.port = app.port, 
	  loss = "lgd.r", 
	  pools = "pool", 
             method = "t.test", 
             alpha = 0.05)