A generalised property exposure rating framework is presented here to address two issues arising in the standard approach to exposure rating, especially in the context of direct insurance and facultative reinsurance (D&F) property pricing:
(a) What to do when the main assumption of exposure rating, scalability – that is, that the probability of a given damage ratio does not depend on the maximum possible loss (MPL) but only on the type of property – breaks down.
(b) How to take account of the uncertainty around the MPL, that is, the fact that the MPL (unlike the insured value, IV) is an informed estimate rather than a contractual feature.
The first difficulty is addressed by making the exposure rating framework more flexible by introducing exposure curves that are a mixture of scale-dependent and scale-independent losses, and where the weight given to the two components is a function of the MPL. This allows to model the impact on the expected losses of changes in the underlying deductibles, a classic problem in D&F pricing normally solved with the help of deductible impact tables. The second difficulty is addressed by working out the mathematical implications of having a finite probability of exceeding the MPL and extending the exposure curve up to the maximum of MPL and IV. A practical application of this framework – in which the scale-independent and scale-dependent losses are identified with attritional and large losses respectively – is described. A discussion of how this generalised framework can be calibrated based on actual data is included, and implementation code for the framework is made available.
