Welcome to the chainladder quickstart guide. This tutorial will walk you through basic functionality of the chainladder package.
Import the package just like any other. We will also include the popular pandas and numpy packages to complete this tutorial.
import chainladder as cl
import numpy as np
import pandas as pdIn order to use the functionality of the package, we need data. Specifically, we need loss data that can be represented in triangle form. The current release of chainladder does not include any data pre-processing functionality. Instead it relies on data in the form of the popular pandas.DataFrame. Data can be either tabular or already summarized in triangular form.
The chainladder package comes pre-installed with a few generic
datasets which we will access using the load_dataset function. For
the complete list, you can find them here. We will
be using the Reinsurance Association of America (RAA) triangle.
RAA = cl.load_dataset('RAA')
RAA.round(0)| dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| origin | ||||||||||
| 1981 | 5012 | 8269.0 | 10907.0 | 11805.0 | 13539.0 | 16181.0 | 18009.0 | 18608.0 | 18662.0 | 18834.0 |
| 1982 | 106 | 4285.0 | 5396.0 | 10666.0 | 13782.0 | 15599.0 | 15496.0 | 16169.0 | 16704.0 | NaN |
| 1983 | 3410 | 8992.0 | 13873.0 | 16141.0 | 18735.0 | 22214.0 | 22863.0 | 23466.0 | NaN | NaN |
| 1984 | 5655 | 11555.0 | 15766.0 | 21266.0 | 23425.0 | 26083.0 | 27067.0 | NaN | NaN | NaN |
| 1985 | 1092 | 9565.0 | 15836.0 | 22169.0 | 25955.0 | 26180.0 | NaN | NaN | NaN | NaN |
| 1986 | 1513 | 6445.0 | 11702.0 | 12935.0 | 15852.0 | NaN | NaN | NaN | NaN | NaN |
| 1987 | 557 | 4020.0 | 10946.0 | 12314.0 | NaN | NaN | NaN | NaN | NaN | NaN |
| 1988 | 1351 | 6947.0 | 13112.0 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 1989 | 3133 | 5395.0 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 1990 | 2063 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
The RAA data is still just a DataFrame, and needs to be turned into a triangle object. Once we do this, we can perform various calculations on the triangle, such as converting a cumulative triangle to incremental or or representing the data in tabular form.
Incremental triangle
RAA_Triangle = cl.Triangle(RAA)
RAA_Triangle.cum2incr()| dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| origin | ||||||||||
| 1981 | 5012 | 3257.0 | 2638.0 | 898.0 | 1734.0 | 2642.0 | 1828.0 | 599.0 | 54.0 | 172.0 |
| 1982 | 106 | 4179.0 | 1111.0 | 5270.0 | 3116.0 | 1817.0 | -103.0 | 673.0 | 535.0 | NaN |
| 1983 | 3410 | 5582.0 | 4881.0 | 2268.0 | 2594.0 | 3479.0 | 649.0 | 603.0 | NaN | NaN |
| 1984 | 5655 | 5900.0 | 4211.0 | 5500.0 | 2159.0 | 2658.0 | 984.0 | NaN | NaN | NaN |
| 1985 | 1092 | 8473.0 | 6271.0 | 6333.0 | 3786.0 | 225.0 | NaN | NaN | NaN | NaN |
| 1986 | 1513 | 4932.0 | 5257.0 | 1233.0 | 2917.0 | NaN | NaN | NaN | NaN | NaN |
| 1987 | 557 | 3463.0 | 6926.0 | 1368.0 | NaN | NaN | NaN | NaN | NaN | NaN |
| 1988 | 1351 | 5596.0 | 6165.0 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 1989 | 3133 | 2262.0 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 1990 | 2063 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
Triangle in tabular form
RAA_Triangle.dataAsTable().head()| origin | dev | values |
|---|---|---|
| 1981 | 1 | 5012.0 |
| 1982 | 1 | 106.0 |
| 1983 | 1 | 3410.0 |
| 1984 | 1 | 5655.0 |
| 1985 | 1 | 1092.0 |
To use basic chainladder functionality, we will rely on the ChainLadder class. This is a class that expands on the triangle class and includes features about loss development (using chainladder techniques, of course). To create a chainladder object, you will need to supply a triangle object.
From above, we will supply our RAA_Triangle object, and look at a quick age-to-age summary using the ata() method.
RAA_CL = cl.ChainLadder(RAA_Triangle)
RAA_CL.ata()| origin | 1-2 | 2-3 | 3-4 | 4-5 | 5-6 | 6-7 | 7-8 | 8-9 | 9-10 | 10-Ult |
|---|---|---|---|---|---|---|---|---|---|---|
| 1981 | 1.649840 | 1.319023 | 1.082332 | 1.146887 | 1.195140 | 1.112972 | 1.033261 | 1.002902 | 1.009217 | NaN |
| 1982 | 40.424528 | 1.259277 | 1.976649 | 1.292143 | 1.131839 | 0.993397 | 1.043431 | 1.033088 | NaN | NaN |
| 1983 | 2.636950 | 1.542816 | 1.163483 | 1.160709 | 1.185695 | 1.029216 | 1.026374 | NaN | NaN | NaN |
| 1984 | 2.043324 | 1.364431 | 1.348852 | 1.101524 | 1.113469 | 1.037726 | NaN | NaN | NaN | NaN |
| 1985 | 8.759158 | 1.655619 | 1.399912 | 1.170779 | 1.008669 | NaN | NaN | NaN | NaN | NaN |
| 1986 | 4.259749 | 1.815671 | 1.105367 | 1.225512 | NaN | NaN | NaN | NaN | NaN | NaN |
| 1987 | 7.217235 | 2.722886 | 1.124977 | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 1988 | 5.142117 | 1.887433 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| 1989 | 1.721992 | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN | NaN |
| simple | 8.206099 | 1.695894 | 1.314510 | 1.182926 | 1.126962 | 1.043328 | 1.034355 | 1.017995 | 1.009217 | 1.0 |
| vol-wtd | 2.999359 | 1.623523 | 1.270888 | 1.171675 | 1.113385 | 1.041935 | 1.033264 | 1.016936 | 1.009217 | 1.0 |
| Selected | 2.999359 | 1.623523 | 1.270888 | 1.171675 | 1.113385 | 1.041935 | 1.033264 | 1.016936 | 1.009217 | 1.0 |
The ChainLadder class has a parameter delta. This is described by Barnett/Zenwirth, and the default value is 1 and corresponds to a volume-weighted loss development factor (LDF) pick.
You can directly play with the chainladder model attributes to get things such as ldfs, cdfs, and complete triangles.
LDFs
LDF = pd.Series([ldf.coef_ for ldf in RAA_CL.models], index=RAA_CL.ata().columns)
LDF.round(4)1-2 2.9994 2-3 1.6235 3-4 1.2709 4-5 1.1717 5-6 1.1134 6-7 1.0419 7-8 1.0333 8-9 1.0169 9-10 1.0092 dtype: float64
CDFs
CDF = LDF[::-1].cumprod()[::-1]
CDF.round(4)1-2 8.9202 2-3 2.9740 3-4 1.8318 4-5 1.4414 5-6 1.2302 6-7 1.1049 7-8 1.0604 8-9 1.0263 9-10 1.0092 dtype: float64
Completed Triangle
RAA_CL.predict().round(0)| dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ult |
|---|---|---|---|---|---|---|---|---|---|---|---|
| origin | |||||||||||
| 1981 | 5012 | 8269.0 | 10907.0 | 11805.0 | 13539.0 | 16181.0 | 18009.0 | 18608.0 | 18662.0 | 18834.0 | 18834.0 |
| 1982 | 106 | 4285.0 | 5396.0 | 10666.0 | 13782.0 | 15599.0 | 15496.0 | 16169.0 | 16704.0 | 16858.0 | 16858.0 |
| 1983 | 3410 | 8992.0 | 13873.0 | 16141.0 | 18735.0 | 22214.0 | 22863.0 | 23466.0 | 23863.0 | 24083.0 | 24083.0 |
| 1984 | 5655 | 11555.0 | 15766.0 | 21266.0 | 23425.0 | 26083.0 | 27067.0 | 27967.0 | 28441.0 | 28703.0 | 28703.0 |
| 1985 | 1092 | 9565.0 | 15836.0 | 22169.0 | 25955.0 | 26180.0 | 27278.0 | 28185.0 | 28663.0 | 28927.0 | 28927.0 |
| 1986 | 1513 | 6445.0 | 11702.0 | 12935.0 | 15852.0 | 17649.0 | 18389.0 | 19001.0 | 19323.0 | 19501.0 | 19501.0 |
| 1987 | 557 | 4020.0 | 10946.0 | 12314.0 | 14428.0 | 16064.0 | 16738.0 | 17294.0 | 17587.0 | 17749.0 | 17749.0 |
| 1988 | 1351 | 6947.0 | 13112.0 | 16664.0 | 19525.0 | 21738.0 | 22650.0 | 23403.0 | 23800.0 | 24019.0 | 24019.0 |
| 1989 | 3133 | 5395.0 | 8759.0 | 11132.0 | 13043.0 | 14521.0 | 15130.0 | 15634.0 | 15898.0 | 16045.0 | 16045.0 |
| 1990 | 2063 | 6188.0 | 10046.0 | 12767.0 | 14959.0 | 16655.0 | 17353.0 | 17931.0 | 18234.0 | 18402.0 | 18402.0 |
Well done on getting through the quickstart tutorial where we've covered basic triangle data and chainladder functionality. A more generalized framework to the Chainladder class is the MackChainLadder class which we will review in the next example.