Collection of Tools for LGD Rating Model Development.
LGDtoolkit 0.2.0
LGDtoolkit provides collection of tools for loss given default (LGD) rating model development and validation. Keeping in mind the fact that model development is highly iterative and repetitive process, having standardized and automated tools for this purpose is of the utmost importance for analysts. The main goal of this package is to cover the most common steps of LGD model development. As additional contribution we attempted to add some functionalities which at the moment of the package development were not presented in R package ecosystem in area of credit risk modeling. In the current package version, available functionalities mainly refer to risk factor engineering and multivariate analysis. With a new versions, package will be extended with validation methods and survival analysis for LGD modeling.
The following case study shows the usage of LGDtoolkit package. The study is based on synthetic data which consists of 1200 facilities with closed or substantially closed recovery status. This data set is distributed along with LGDtoolkit package under the data frame lgd.ds.c. Presented examples are simplified, but yet realistic, version of the LGD model development. So, let’s start with a concrete case study.
First, we will import the libraries needed for the following examples.
library(monobin)
library(PDtoolkit)
library(LGDtoolkit)
If the packages are not already installed, run the following code before the library import install.packages(c("monobin", "PDtoolkit", "LGDtoolkit")) to install these packages from the CRAN, while devtools::install_github("andrija-djurovic/LGDtoolkit") to install development version of LGDtoolkit package.
:warning: Be aware that some functions from
PDtoolkitpackage will be masked after importingLGDtoolkitpackage. In order to avoid executing function from the wrong namespace, while running some of the commands we will explicitly add namespace while calling certain function (e.g.PDtoolkit::orLGDtoolkit::).
Then, let’s import and inspect the structure of the modeling data set - lgd.ds.c.
data(lgd.ds.c)
str(lgd.ds.c)
## 'data.frame': 1200 obs. of 20 variables:
## $ lgd : num 0.541 0.857 0.829 0.91 0.857 ...
## $ rf_01: num 6.06 12.68 22.62 11.21 12.68 ...
## $ rf_02: num 111 120 116 111 120 ...
## $ rf_03: num 19.4 45.5 28.9 29.3 45.5 ...
## $ rf_04: num 268 311 343 370 311 ...
## $ rf_05: num 15.88 4.84 64.84 67.05 4.84 ...
## $ rf_06: num NA NA NA NA NA ...
## $ rf_07: num 822 1064 2243 1518 1064 ...
## $ rf_08: num 43.1 86.5 85.4 102 86.5 ...
## $ rf_09: num 6828 4374 3820 3378 4374 ...
## $ rf_10: num 0.0184 0.011 0 0 0.011 ...
## $ rf_11: num NA NA 1.74 1 NA ...
## $ rf_12: num 347 442 903 897 442 ...
## $ rf_13: num 2.74 2.37 3.84 6.05 2.37 ...
## $ rf_14: num 1857 3158 5330 4215 3158 ...
## $ rf_15: num 1239 8651 2385 3530 8651 ...
## $ rf_16: num 14.9 35.8 33.4 35.7 35.8 ...
## $ rf_17: num 732 952 1874 2046 952 ...
## $ rf_18: num 0.0384 0.0109 0.0257 0.0311 0.0109 ...
## $ rf_19: num NA NA NA NA NA ...
From the structure results, we conclude that there are in total 20 variables. All are of numeric type and variable lgd for the further examples will be treated as target variable while all other will be treated as risk factors that compete for the final model.
Usually the first step in model development is the univariate analysis. For this purpose we can use univariate function from the PDtoolkit package:
uni.res <- PDtoolkit::univariate(db = lgd.ds.c, sc.threshold = 0.3)
uni.res
## rf rf.type bin.type bin cnt pct cnt.unique min p1 p5
## 1 lgd numeric complete cases complete cases 1200 1.000000000 615 0.00000000 0.00000000 0.00000000
## 2 rf_01 numeric complete cases complete cases 1200 1.000000000 775 0.00000000 1.00000000 3.99202376
## 3 rf_02 numeric special cases special cases 362 0.301666667 1 Inf NA NA
## 4 rf_02 numeric complete cases complete cases 838 0.698333333 388 17.65574122 23.00000000 23.00000000
## 5 rf_03 numeric special cases special cases 147 0.122500000 1 Inf NA NA
## 6 rf_03 numeric complete cases complete cases 1053 0.877500000 668 1.00444401 2.67928945 7.17500605
## 7 rf_04 numeric special cases special cases 4 0.003333333 1 Inf NA NA
## 8 rf_04 numeric complete cases complete cases 1196 0.996666667 808 22.97083233 28.91797075 48.00000000
## 9 rf_05 numeric special cases special cases 8 0.006666667 1 Inf NA NA
## 10 rf_05 numeric complete cases complete cases 1192 0.993333333 804 4.84052175 17.63929155 30.34240156
## 11 rf_06 numeric special cases special cases 529 0.440833333 1 Inf NA NA
## 12 rf_06 numeric complete cases complete cases 671 0.559166667 448 22.54000000 30.72439938 136.68058281
## 13 rf_07 numeric special cases special cases 593 0.494166667 1 Inf NA NA
## 14 rf_07 numeric complete cases complete cases 607 0.505833333 401 15.28000000 89.63092671 294.53491499
## 15 rf_08 numeric special cases special cases 489 0.407500000 1 Inf NA NA
## 16 rf_08 numeric complete cases complete cases 711 0.592500000 462 25.13532680 37.83857276 46.31208595
## 17 rf_09 numeric special cases special cases 8 0.006666667 1 Inf NA NA
## 18 rf_09 numeric complete cases complete cases 1192 0.993333333 825 28.03553689 331.89336495 1094.16481953
## 19 rf_10 numeric special cases special cases 4 0.003333333 1 Inf NA NA
## 20 rf_10 numeric complete cases complete cases 1196 0.996666667 366 0.00000000 0.00000000 0.00000000
## 21 rf_11 numeric special cases special cases 477 0.397500000 1 Inf NA NA
## 22 rf_11 numeric complete cases complete cases 723 0.602500000 319 1.00000000 1.00000000 1.00000000
## 23 rf_12 numeric special cases special cases 299 0.249166667 1 Inf NA NA
## 24 rf_12 numeric complete cases complete cases 901 0.750833333 610 40.79299196 80.66429745 199.08245061
## 25 rf_13 numeric special cases special cases 56 0.046666667 1 Inf NA NA
## 26 rf_13 numeric complete cases complete cases 1144 0.953333333 647 0.00000000 0.00000000 0.74992761
## 27 rf_14 numeric special cases special cases 174 0.145000000 1 Inf NA NA
## 28 rf_14 numeric complete cases complete cases 1026 0.855000000 691 18.00000000 124.64224900 733.27427502
## 29 rf_15 numeric special cases special cases 139 0.115833333 1 Inf NA NA
## 30 rf_15 numeric complete cases complete cases 1061 0.884166667 723 25.89103169 134.62457345 505.96257390
## 31 rf_16 numeric special cases special cases 339 0.282500000 1 Inf NA NA
## 32 rf_16 numeric complete cases complete cases 861 0.717500000 564 0.01000000 0.01000000 0.02861894
## 33 rf_17 numeric special cases special cases 580 0.483333333 1 Inf NA NA
## 34 rf_17 numeric complete cases complete cases 620 0.516666667 404 9.55715886 143.09429242 323.81487058
## 35 rf_18 numeric complete cases complete cases 1200 1.000000000 514 -0.09558666 -0.09558666 -0.09558666
## 36 rf_19 numeric special cases special cases 539 0.449166667 1 Inf NA NA
## 37 rf_19 numeric complete cases complete cases 661 0.550833333 458 -0.93826545 -0.76718787 -0.34052105
## p25 p50 avg avg.se p75 p95 p99 max
## 1 0.004531067 0.244401597 0.368640404 0.010888824 0.69014569 1.02125333 1.22572992 1.47211318
## 2 13.508624746 22.759283183 33.179850507 0.900671298 39.54558626 108.69964615 139.73265872 163.80808151
## 3 NA NA NaN NA NA NA NA -Inf
## 4 47.000000000 59.000000000 81.316485219 2.082000905 103.06613890 226.56058557 320.71023494 360.00000000
## 5 NA NA NaN NA NA NA NA -Inf
## 6 19.640130269 36.111459262 42.562968628 0.992860052 52.00000000 108.78497380 156.93884055 199.48371485
## 7 NA NA NaN NA NA NA NA -Inf
## 8 177.077454733 436.593547392 378.727003361 6.022114626 549.87086366 664.78662040 720.64942751 754.09840803
## 9 NA NA NaN NA NA NA NA -Inf
## 10 66.108210086 114.212555009 121.242644759 1.904226326 172.97119442 233.18530648 283.95762761 317.67481818
## 11 NA NA NaN NA NA NA NA -Inf
## 12 625.820185630 1410.632064257 3250.742300492 181.967590186 3122.21772118 14658.67581971 19847.22461382 29308.79232210
## 13 NA NA NaN NA NA NA NA -Inf
## 14 974.654821003 2009.935649648 3974.710244391 195.792004653 4531.99322543 15939.16035492 19941.21610207 29308.79232210
## 15 NA NA NaN NA NA NA NA -Inf
## 16 95.575067313 154.273093829 153.191809152 2.694522227 206.04944612 280.20490058 308.72846918 329.36829346
## 17 NA NA NaN NA NA NA NA -Inf
## 18 3451.504760850 6387.968495929 13116.227712964 613.784710353 13209.48701866 48514.01533086 128780.86509465 150300.28736844
## 19 NA NA NaN NA NA NA NA -Inf
## 20 0.000000000 0.006545185 10.640635244 1.023022133 0.11415108 58.09044509 130.20986556 461.89746028
## 21 NA NA NaN NA NA NA NA -Inf
## 22 1.390595321 2.315279280 2.834502108 0.071709573 3.72683737 6.69769043 8.76458372 13.32276060
## 23 NA NA NaN NA NA NA NA -Inf
## 24 481.779871117 800.755212480 1005.618302342 28.532476294 1300.00390340 2393.06723243 4593.25540849 6766.97688547
## 25 NA NA NaN NA NA NA NA -Inf
## 26 2.000000000 3.765871170 5.275372901 0.151600737 6.68620933 16.45878534 24.30283094 40.86986102
## 27 NA NA NaN NA NA NA NA -Inf
## 28 3416.733392077 6663.596192870 12224.057202898 532.214934598 13175.30531341 42107.06794584 64345.04989650 182966.46247162
## 29 NA NA NaN NA NA NA NA -Inf
## 30 1858.723619660 4377.230297497 13880.543882895 1079.015094266 10636.51117503 57333.54421848 107806.99697343 388956.22094669
## 31 NA NA NaN NA NA NA NA -Inf
## 32 4.284460905 18.632123177 30.669779411 1.483646270 37.92775639 119.76771245 232.96024267 256.28195529
## 33 NA NA NaN NA NA NA NA -Inf
## 34 1382.595945211 2822.068110305 6015.401565964 375.345422508 5769.98378543 22575.55870222 47254.26489318 63442.87624218
## 35 -0.016089693 0.006024786 0.002922821 0.001223155 0.03216825 0.06317923 0.07584763 0.08204055
## 36 NA NA NaN NA NA NA NA -Inf
## 37 -0.183700732 -0.084087004 -0.016573987 0.015850496 -0.01772558 0.65758039 1.76506460 3.29046060
## neg pos cnt.outliers sc.ind
## 1 0 957 0 0
## 2 0 1196 118 0
## 3 NA NA 0 1
## 4 0 838 60 1
## 5 NA NA 0 0
## 6 0 1053 61 0
## 7 NA NA 0 0
## 8 0 1196 0 0
## 9 NA NA 0 0
## 10 0 1192 0 0
## 11 NA NA 0 1
## 12 0 671 103 1
## 13 NA NA 0 1
## 14 0 607 72 1
## 15 NA NA 0 1
## 16 0 711 0 1
## 17 NA NA 0 0
## 18 0 1192 114 0
## 19 NA NA 0 0
## 20 0 655 279 0
## 21 NA NA 0 1
## 22 0 723 20 1
## 23 NA NA 0 0
## 24 0 901 41 0
## 25 NA NA 0 0
## 26 0 1126 86 0
## 27 NA NA 0 0
## 28 0 1026 121 0
## 29 NA NA 0 0
## 30 0 1061 141 0
## 31 NA NA 0 0
## 32 0 861 67 0
## 33 NA NA 0 1
## 34 0 620 81 1
## 35 532 668 87 0
## 36 NA NA 0 1
## 37 514 147 95 1
Based on the results we can see that univariate treats differently so-called special and complete cases. Additionally, we can conclude that there are some risk factors with share of special cases higher than 30% and they will be excluded from the further analysis.
:warning: In the previous example threshold of 30% for the missing cases is selected for the sake of package demo, but in practice greater attention is paid on meaning and dealing with those values.
rf.excl <- unique(uni.res$rf[uni.res$sc.ind%in%1])
rf.excl
## [1] "rf_02" "rf_06" "rf_07" "rf_08" "rf_11" "rf_17" "rf_19"
lgd.ds.c <- lgd.ds.c[, !names(lgd.ds.c)%in%rf.excl]
For result details and additional arguments of univariate function check help page ?PDtoolkit::univariate.
Sometimes, when building LGD models numeric risk factors are discretized, so we will proceed next with that step. For the purpose of binning the numeric risk factors, we will use one of the functions (sts.bin) from the monobin package. Details about this package can be found here. Usually before this step modelers split data set on training and testing and perform binning (and other model development steps) only on training data set. For the sake of simplicity, for this case study we will skip this part but modelers should be aware of importance of data set splitting step.
#define target variable and exclude it from the binning process
target <- "lgd"
num.rf <- names(lgd.ds.c)[!names(lgd.ds.c)%in%target]
lgd.ds.c[, num.rf] <- sapply(num.rf, function(x)
monobin::ndr.bin(x = lgd.ds.c[, x], y = lgd.ds.c[, target])[[2]])
str(lgd.ds.c)
## 'data.frame': 1200 obs. of 13 variables:
## $ lgd : num 0.541 0.857 0.829 0.91 0.857 ...
## $ rf_01: chr "01 (-Inf,20.1001)" "01 (-Inf,20.1001)" "02 [20.1001,Inf)" "01 (-Inf,20.1001)" ...
## $ rf_03: chr "02 [14.4975,70.6008)" "02 [14.4975,70.6008)" "02 [14.4975,70.6008)" "02 [14.4975,70.6008)" ...
## $ rf_04: chr "03 [142.6312,531.6402)" "03 [142.6312,531.6402)" "03 [142.6312,531.6402)" "03 [142.6312,531.6402)" ...
## $ rf_05: chr "01 (-Inf,38.408)" "01 (-Inf,38.408)" "02 [38.408,177.9077)" "02 [38.408,177.9077)" ...
## $ rf_09: chr "01 (-Inf,25891.4584)" "01 (-Inf,25891.4584)" "01 (-Inf,25891.4584)" "01 (-Inf,25891.4584)" ...
## $ rf_10: chr "02 [0.0157,55.8871)" "01 (-Inf,0.0157)" "01 (-Inf,0.0157)" "01 (-Inf,0.0157)" ...
## $ rf_12: chr "01 (-Inf,1354.0616)" "01 (-Inf,1354.0616)" "01 (-Inf,1354.0616)" "01 (-Inf,1354.0616)" ...
## $ rf_13: chr "03 [2.6617,5.0394)" "02 [1,2.6617)" "03 [2.6617,5.0394)" "04 [5.0394,Inf)" ...
## $ rf_14: chr "02 [1698.4647,10839.1025)" "02 [1698.4647,10839.1025)" "02 [1698.4647,10839.1025)" "02 [1698.4647,10839.1025)" ...
## $ rf_15: chr "02 [825.8567,3825.6754)" "03 [3825.6754,Inf)" "02 [825.8567,3825.6754)" "02 [825.8567,3825.6754)" ...
## $ rf_16: chr "02 [0.0634,34.6935)" "03 [34.6935,43.6851)" "02 [0.0634,34.6935)" "03 [34.6935,43.6851)" ...
## $ rf_18: chr "03 [-0.0208,0.0506)" "03 [-0.0208,0.0506)" "03 [-0.0208,0.0506)" "03 [-0.0208,0.0506)" ...
After completing binning step, modelers usually perform bivariate analysis and start examination of discriminatory power of risk factors in relation with target variable. Probably the most common metric used for this purpose is coefficient determination (R squared) and it usually used for further risk factor filtering. In order to calculate R squared we will use function r.squared from LGDtoolkit package.
LGDtoolkit::r.squared(db = lgd.ds.c, target = target)
## rf rf.type miss.inf miss.inf.pct r.squared
## 1 rf_01 character 0 0 0.04520316
## 2 rf_03 character 0 0 0.04445570
## 3 rf_04 character 0 0 0.05649746
## 4 rf_05 character 0 0 0.08701528
## 5 rf_09 character 0 0 0.03057418
## 6 rf_10 character 0 0 0.06067633
## 7 rf_12 character 0 0 0.05918994
## 8 rf_13 character 0 0 0.05806014
## 9 rf_14 character 0 0 0.02408769
## 10 rf_15 character 0 0 0.06974936
## 11 rf_16 character 0 0 0.08610673
## 12 rf_18 character 0 0 0.04049297
Due to the fact that we do not have too many available risk factors, we will not perform additional filtering based on the results of above bivariate analysis. Thus we move on to multivariate analysis. For this purpose LGDtoolkit package is equipped with two customized stepwise algorithms stepFWD and stepRPC. Both functions support standard OLS regression as well as fractional logistic regression. Note that latter regression type requires target variable to be between 0 and 1. For the following example we will use stepFWD with OLS estimation method. Analysts are also encouraged to check the help page of both function as well as other customized blockwise regression (?LGDtoolkit:: staged.blocks, ?LGDtoolkit:: embedded.blocks, ?LGDtoolkit:: ensemble.blocks)
mv.res <- LGDtoolkit::stepFWD(start.model = lgd ~ 1,
p.value = 0.05,
db = lgd.ds.c,
reg.type = "ols")
## [1] "Running iteration: 1"
## [1] "Running iteration: 2"
## [1] "Running iteration: 3"
## [1] "Running iteration: 4"
## [1] "Running iteration: 5"
## [1] "Running iteration: 6"
## [1] "Running iteration: 7"
names(mv.res)
## [1] "model" "steps" "warnings" "dev.db"
summary(mv.res$model)$coefficients
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.31472806 0.05800282 5.4260820 0.0000000698208174489
## rf_0502 [38.408,177.9077) -0.15113159 0.03699533 -4.0851537 0.0000470138750068009
## rf_0503 [177.9077,Inf) -0.31736141 0.04253544 -7.4611054 0.0000000000001656480
## rf_05SC -0.39272911 0.12412552 -3.1639676 0.0015959938925431542
## rf_0102 [20.1001,Inf) -0.05813067 0.02256450 -2.5762008 0.0101096786738615555
## rf_1602 [0.0634,34.6935) 0.22012105 0.03886414 5.6638601 0.0000000185689455348
## rf_1603 [34.6935,43.6851) 0.31049170 0.05299670 5.8586987 0.0000000060405748407
## rf_1604 [43.6851,Inf) 0.34576836 0.04745510 7.2862216 0.0000000000005809151
## rf_16SC 0.14966225 0.04049960 3.6954006 0.0002295802574621863
## rf_0302 [14.4975,70.6008) -0.06459748 0.03365298 -1.9195176 0.0551591686509560614
## rf_0303 [70.6008,Inf) -0.19066308 0.04244148 -4.4923757 0.0000077329442034241
## rf_03SC -0.11375612 0.04283670 -2.6555763 0.0080236864779808167
## rf_1502 [825.8567,3825.6754) 0.08273906 0.03688639 2.2430781 0.0250763047068701603
## rf_1503 [3825.6754,Inf) 0.12446684 0.03663231 3.3977339 0.0007020626257604785
## rf_15SC 0.02916156 0.04336299 0.6724989 0.5013974803005729619
## rf_1202 [1354.0616,Inf) 0.10378840 0.03101615 3.3462693 0.0008447905530221169
## rf_12SC 0.10780106 0.02603006 4.1414064 0.0000369702534436035
mv.res$steps
## rf aic p.val p.val.check trend.check
## 1 rf_05 -2442.196 0.00000000000000000000 TRUE TRUE
## 2 rf_01 -2468.610 0.00000000000000000000 TRUE TRUE
## 3 rf_16 -2568.960 0.00000000000000000000 TRUE TRUE
## 4 rf_03 -2593.788 0.00000000000000000000 TRUE TRUE
## 5 rf_15 -2612.353 0.00000000000000000000 TRUE TRUE
## 6 rf_12 -2630.565 0.00000000000002375877 TRUE TRUE
summary(mv.res$model)$r.squared
## [1] 0.236374
:warning: Be aware that usually in practice greater attention is paid on dealing with special cases and missing values before running multivariate analysis. Sometimes they are merged with one of the modalities from so-called complete cases. In above example this procedure was not performed, but if analysts want to run this step it can be done using function
LGDtoolkit::sc.merge. For details check the help page.
After selecting the final model set of validation procedures are performed. For time being LGDtoolkit package has LGDtoolkit::kfold.vld and LGDtoolkit::kfold.idx functions that can be used for validating some of goodness-of-fit metrics, but with a new versions of the package this area will be extended with additional tests. In order to apply CV validation analysts can run the following code:
LGDtoolkit::kfold.vld(model = mv.res$model, k = 10, seed = 1984)
## $iter
## k no amse rmse r.squared
## 1 1 120 0.11474930 0.3387467 0.1843044
## 2 2 120 0.08741986 0.2956685 0.2764421
## 3 3 120 0.12021084 0.3467143 0.3273682
## 4 4 120 0.11124528 0.3335345 0.2475501
## 5 5 120 0.12221417 0.3495914 0.1768010
## 6 6 120 0.11106522 0.3332645 0.2694624
## 7 7 120 0.11170662 0.3342254 0.1644091
## 8 8 120 0.11181607 0.3343891 0.1627783
## 9 9 120 0.11101191 0.3331845 0.2782350
## 10 10 120 0.12080593 0.3475715 0.1367292
##
## $summary
## amse rmse r.squared
## 1 0.1122245 0.334689 0.222408