Pricing in General Insurance

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21

Exposure Rating for Property

Exposure method is a method to price an insurance policy when the data for a specic cli-

ent is not sufcient to produce a reliable severity model. It is based on the use of so-called

‘exposure curves’, which are reengineered severity curves and are usually based on losses

from a large number of clients, as collected by large institutions such as Lloyd’s of London

or Swiss Re. Ultimately, however, the origins of many of the exposure curves used by

underwriters and actuaries in the London market remain mysterious. Actuaries would do

well not to consider these curves too dogmatically despite their widespread use.

Exposure curves are typically used in property reinsurance, for example, to price a Risk

XL policy. However, there is no particular reason why they can’t be used in direct insur-

ance in tandem with a frequency estimate to produce a stochastic loss model.

Before we move on to describe how exposure curves arise (Section 21.2) and how they

can be used to price (re)insurance, it is perhaps useful to take a step back and consider how

one would go about pricing property risks if one knew nothing about exposure curves

(Section 21.1).

21.1 Inadequacy of Standard Experience Rating for Property Risks

One way to price property risk for a portfolio of property is of course to use experience

rating: collect all losses over a certain period, produce a frequency model and a severity

model, and combine them with a Monte Carlo simulation or a similar method. This is a

legitimate method if there is enough data. However, it requires some care:

1. When producing a severity model, we must make sure that no loss can be gener-

ated that exceeds the value of the most expensive property in the portfolio: in

other words, the severity distribution must be capped. Although this correction is

needed, it is probably insufcient – we are basically saying that the only informa-

tion we need for experience rating about the value of the properties is the value of

the most expensive one. Surely, the other properties should play some role in the

choice of the severity model?

2. Producing a realistic severity model is difcult. More than in other lines of busi-

ness, loss data sets tend to be characterised by many small losses with (possi-

bly) a few large spikes corresponding to buildings being completely destroyed or

severely damaged. As a result, if the client has been lucky enough that it has not

had very large losses (let us say losses corresponding to the total loss of a prop-

erty), the severity model will signicantly underestimate the chance of a large

loss. On the other hand, if the client has experienced a catastrophic loss, the empir-

ical severity distribution may be completely dominated by such a loss. It is very

difcult to get the balance right unless a very large loss data set is available.