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Actuarial Science and Insurance Series: insurance-and-pensions

What is wrong with the chain ladder technique (?)

The title is both a statement and a question, and in the talk you will find a list of things that are wrong with the chain ladder technique but also a question asking whether it is so bad after all.

Author(s): Professor Richard Verrall - Cass Business School;

The title is both a statement and a question, and in the talk you will find a list of things that are wrong with the chain ladder technique but also a question asking whether it is so bad after all! In fact, the chain ladder technique has a lot going for it - it is simple, it is widely used and it is pretty well understood. However, it has some significant faults: for example, the fact that it does not include any calendar year effects. More fundamentally, it is just a technique (an algorithm) for filling in the rest of a rectangle when you just have data in the upper left corner. It doesn't use any risk theory; it doesn't make any assumptions about the way the data have been generated; and the parameters amalgamate changes that are due to a variety of different sources. In all other areas of actuarial science, it is usual to consider the mechanisms generating the data and build models using these fundamental principles. For example, in rating it is common to use data on claims frequency and claims severity and then consider carefully what the results tell you before deciding how to set next year's premiums.

In the talk, I explain how it is possible to consider reserving models from first principles as well, and yet retain the appealing simplicity of the chain ladder technique. Using just one extra triangle, it is possible to separate out the payment delay from the reporting delay. This might be very important because it is quite possible for these to have different characteristics over time. So, just like in premium rating, it is possible to make informed decisions about the likely future properties of these delays, and thereby set reasonable (and justifiable) assumptions for any solvency and capital models. Instead of using an ad hoc method, and making ad hoc adjustments, it is possible to use an approach which uses real quantities which have a physical interpretation.

There are 3 papers associated with this talk. The first two ("Prediction of RBNS and IBNR claims using claim amounts and claim counts" and "Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers") describe the basic model which is used as an alternative to the chain ladder technique. The third paper ("Double Chain Ladder") is an extension of the basic model, and is very closely related to the standard chain ladder model. In fact, it shows that (if certain choices are made about the model and the estimation) it is possible to get exactly the same results as the standard chain ladder model. It could be argued therefore, that this model is an alternative stochastic model for the chain ladder model.

The new models have some further advantages. For example, they separate out the RBNS and the IBNR reserves, and they produce a tail, beyond the latest development year, without having to make any further assumptions.

Copyright 2010 by ASTIN Bulletin and PEETERS s.a.. Reproduced with Permission

Attachment(s)
{Spreadsheet - Double Chain Ladder}{https://www.cass.city.ac.uk/__data/assets/excel_doc/0004/368833/doublechainladder.xls}; {Spreadsheet - Estimation}{https://www.cass.city.ac.uk/__data/assets/excel_doc/0005/368834/estimation.xls}; {Double Chain Ladder}{https://www.cass.city.ac.uk/__data/assets/pdf_file/0006/368835/doublechainladder.pdf}; {Cash flow simulation for a model of outstanding liabilities based on claim amounts and claim numbers}{https://www.cass.city.ac.uk/__data/assets/pdf_file/0007/368836/cash-flow-simulation.pdf}; {Prediction of RBNS and IBNR claims using claim amounts and claim counts}{https://www.cass.city.ac.uk/__data/assets/pdf_file/0008/368837/prediction-of-rbns-and-ibnr-claims.pdf}
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