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 and numpy package. For plotting purposes, we will also be using
Jupyter’s %matplotlib inline magic function to render the plots.
In this tutorial we will use industry data from the LOSS RESERVING DATA PULLED FROM NAIC SCHEDULE P
import chainladder as cl
import pandas as pd
import numpy as np
%matplotlib inline
The CAS Loss Reserving incurred data is schedule P data and would include include IBNR. Additionally, the database includes the completed triangles (i.e. the latest accident year has valuations at age 10 years). We will focus on Workers' Compensation data.
We will: - Read in the data - Devlop a case incurred metric - Summarize data across all carriers - Retain age 10 actual case incurred - Eliminate known data beyond year end of 1997
# Read in the data
CAS = pd.read_csv(r'http://www.casact.org/research/reserve_data/wkcomp_pos.csv')
# Devlop a case incurred metric
CAS['INC_LOSS'] = CAS['IncurLoss_D']-CAS['BulkLoss_D']
# Summarize data across all carriers
WCTri = pd.pivot_table(data=CAS, values='INC_LOSS', index=['AccidentYear'],columns=['DevelopmentLag'], aggfunc=np.sum)
WCTri.columns = [str(item) for item in WCTri.columns]
# Retain age 10 actual case incurred
Ult10_values = WCTri.iloc[:,-1]
# Eliminate known data beyond year end of 1997
WCTri=pd.DataFrame(np.array(WCTri)*np.array([np.append(np.array([1]*(len(WCTri)-i)),np.array([np.nan]*i)) for i in range(len(WCTri))]),
index = WCTri.index, columns=WCTri.columns)
cl.Triangle(WCTri).plot()
<matplotlib.figure.Figure at 0x2628e2514a8>
BS = cl.BootChainladder(WCTri, n_sims=50000)
The bootstrap model plots provide various diagnotics to enable a better understanding of the distribution of carried IBNR.
BS.plot()
<matplotlib.figure.Figure at 0x2628e9ae630>
We should expect enough credibility/stability in industrywide data that the Chainladder method is a reasonably good model for developing the triangle. We will use the Bootstrap mean ultimates to test this. As the Bootstrap model was fit without a tail, the ultimate represents age 10 Expected Incurred amount.
print('Case Incurred Actual vs Bootstrap Expected gap at age 10 is '
+ str(round(np.sum(Ult10_values - BS.summary()['Mean Ultimate'].round(0))/np.sum(Ult10_values)*100,2))
+'% of total case inurred at age 10')
(Ult10_values - BS.summary()['Mean Ultimate'].round(0))/Ult10_values
Case Incurred Actual vs Bootstrap Expected gap at age 10 is 0.35% of total case inurred at age 10
AccidentYear 1988 0.000000 1989 0.003534 1990 0.005089 1991 0.004941 1992 0.011566 1993 0.003519 1994 0.018664 1995 0.009364 1996 0.000490 1997 -0.024164 dtype: float64