Introduction

One of the most common ways in which risks can be quantified is through the use of models. Models are mathematical representations of real-world processes. This does not mean that all models should attempt to exactly replicate the way in which the real world works – they are, after all, only models. However, it is important that models are appropriate for the uses to which they are put, and that any limitations of models are recognised. This is particularly important if a model designed for one purpose is being considered for another. Similarly, models calibrated using data in a particular range may not be appropriate for data outside those ranges – a model designed when asset price movements are small may break down when volatility increases. Appropriateness will also differ from organisation to organisation. A model appropriate for analysing the large annuity book of one insurer may give unrealistic answers if used with the smaller annuity book of a competitor.

Even if a model is deemed appropriate for the use to which it is put, uncertainty still remains. The structure of most models is a matter of preference, and the parameters chosen will depend on the exact period and type of data used. This uncertainty should be reflected by considering a range of structures and parameters, and analysing the extent to which changes affect the outputs of the model. This gives a guide as to how robust a model is. In particular, the structure of a model that gives significantly different outputs when calibrated using different data ranges should be reconsidered.

The complexity of models is a difficult area. In some areas, such as derivatives trading, models can grow ever more complex in order to exploit ever smaller pricing anomalies. However, in most areas of risk management greater complexity is not necessarily desirable. First, it makes checking the structure of models more difficult, and it is important that models are independently checked and are comprehensively documented. Greater complexity also makes models more difficult to explain to clients, regulators, senior management and other stakeholders, and it is important that these stakeholders do understand exactly what is going on rather than relying on the output from a ‘black box’. This leads to a third concern, that greater complexity can lead to greater confidence in the ability of a model to reflect the exact nature of risks.