Now we will explore the properties and methods underlying the Munich Chainladder class.
As usual, we we import the chainladder package as well as the popular
pandas package. For plotting purposes, we will also be using Jupyter's
%matplotlib inline magic function.
import chainladder as cl
import pandas as pd
%matplotlib inline
The Munich chainladder method is useful when both a paid and incurred triangle are available. It is an improvement on the standard chainladder in that it considers the ratio of Paid/Incurred (P/I) triangle to adjust both the paid and incurred ultimates. A nice property of the Munich chainladder method is that the (P/I) ratio approaches 1.0 as the development period approaches ultimate. This makes the Paid ultimate and Incurred ultimate converge towards the same value, a property not found in the basic chainladder method.
The chainladder package comes loaded with MCLincurred and
MCLpaid datasets to illustrate the Munich Chainladder method. We
will load these and verify that the (P/I) ratios approach 1.0
MCL_inc = cl.load_dataset('MCLincurred')
MCL_paid = cl.load_dataset('MCLpaid')
MCL_paid/MCL_inc
| dev | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| origin | |||||||
| 1 | 0.588957 | 0.857414 | 0.923149 | 0.944030 | 0.954002 | 0.963336 | 0.980221 |
| 2 | 0.469631 | 0.763323 | 0.876723 | 0.900000 | 0.910686 | 0.956805 | NaN |
| 3 | 0.486226 | 0.863114 | 0.905066 | 0.960000 | 0.967700 | NaN | NaN |
| 4 | 0.652770 | 0.888218 | 0.942998 | 0.952458 | NaN | NaN | NaN |
| 5 | 0.664296 | 0.773863 | 0.957955 | NaN | NaN | NaN | NaN |
| 6 | 0.545799 | 0.910123 | NaN | NaN | NaN | NaN | NaN |
| 7 | 0.407009 | NaN | NaN | NaN | NaN | NaN | NaN |
The Munich chainladder model, unlike the Mack model, only allows for volume-weighted link-ratios. As such, there is no alpha parameter. Like the Mack model, we do have the option of specifying exponential tail fits to our data, but for the purposes of this tutorial we will allow the tails to default to 1.0.
MCL = cl.MunichChainladder(MCL_paid, MCL_inc)
The summary shows that the Ult. Paid and Ult. Incurred are indeed very close, with paids slightly less than incurred.
MCL.summary()
| origin | Latest Paid | Latest Incurred | Latest P/I Ratio | Ult. Paid | Ult. Incurred | P/I Ratio |
|---|---|---|---|---|---|---|
| 1 | 2131.0 | 2174.0 | 0.980221 | 2131.000000 | 2174.000000 | 0.980221 |
| 2 | 2348.0 | 2454.0 | 0.956805 | 2384.842092 | 2443.222400 | 0.976105 |
| 3 | 4494.0 | 4644.0 | 0.967700 | 4553.623621 | 4634.357895 | 0.982579 |
| 4 | 5850.0 | 6142.0 | 0.952458 | 6069.509293 | 6182.347407 | 0.981748 |
| 5 | 4648.0 | 4852.0 | 0.957955 | 4878.950383 | 4957.805406 | 0.984095 |
| 6 | 4010.0 | 4406.0 | 0.910123 | 4598.995746 | 4672.401782 | 0.984289 |
| 7 | 2044.0 | 5022.0 | 0.407009 | 7504.575860 | 7655.377611 | 0.980301 |
We can see that the basic chainladder does not guarantee that the paid and incurred ratios converge to 1.0, with the below data ranging from a low of 0.73 to a high of 1.11.
MCL.plot(plots=['PI1','PI2'])
<matplotlib.figure.Figure at 0x221b68f0080>
The Munich model's effect on ultimates can be drastic by origin year. For this data, a paid Mack approach would understand the latest origin period relative to both the Munich method and the Mack Incurred ultimate.
MCL.plot(plots=['MCLvsMackpaid','MCLvsMackinc'])
<matplotlib.figure.Figure at 0x221b753fa20>
Not specifying plots will render a view similar to the chainladder package in R which includes residual graphs.
MCL.plot()
<matplotlib.figure.Figure at 0x221b7043860>
