Pricing in General Insurance

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11

Burning Cost Analysis

Despite its simplicity and its many limitations, burning cost analysis is one of the most

widespread pricing techniques, especially in such contexts as the London Market. It is

an estimate of the expected losses to a policy (gross, ceded and retained) based on an

average of the claims experience in past years, possibly with corrections/adjustments to

take claims ination, changes in exposure and in risk prole, allowance for large losses,

incurred but not reported (IBNR) claims, expected changes in reserve and so on, but with-

out any explicit modelling. It therefore builds up on the data summarisation exercise that

we described in Section 10.3.

We have already come across a rudimentary example of burning cost analysis in Chapter

2, ‘An elementary pricing example’: we were given total losses incurred over a number of

years. We then brought each year into current terms by revaluing them by claims ina-

tion and by adjusting them to current exposure estimates and to the current risk prole.

We excluded the most recent year because of IBNR, then we averaged everything and we

took 95% of the average because the cover was a quota share cover that paid only 95% of

each claim. The result was the burning cost of the claims. In this chapter, we will see how

this can be improved upon by making full use of the individual claims and not only of

the aggregate losses for each policy year, allowing us to cost policies with individual loss

modiers such as deductibles and limits.

Burning cost analysis is perhaps as far as one gets towards costing a risk and its vola-

tility without resorting to stochastic modelling: and it is surprising how much one can

achieve by that. Burning cost analysis can be used as a pricing technique in its own right

but can also be used to provide a different estimate of the cost of risk alongside frequency/

severity modelling analysis. This will have several advantages:

• It will provide a sense-check on the results of frequency/severity modelling.

When the results for the basic statistics such as the mean and the volatility differ

signicantly between the two methods, this might indicate a mistake in one of the

methods or, as it often happens, the difference might be used to explain the added

value of frequency/severity modelling.

• The results of the burning cost analysis can be used as an intermediate step

between the initial summary statistics and the results of frequency/severity mod-

elling to communicate the results of frequency/severity modelling and have the

client’s or the underwriter’s buy-in.

There is very little theory behind burning cost analysis and this technique is best learnt

with examples. We will therefore explain it step by step with the aid of a case study. The

data set for this case study can be found on the book’s website.