Statistical Quality Standards: Challenges in Internal Model Implementation

Markus Bellion, Christopher Lotz and Peter Müller

Statistical quality standards stand out among the internal model test and standards as they address the core of the matter, the internal model in the narrow sense.¹¹ For a definition of an internal model in the narrow sense, see Chapter 1. They do not primarily take on the perspective of model purpose or model use (in contrast, for example, to the use test and the calibration standards).²² For further details about the use test and calibration standards, see Chapters 6 and 9. The regulatory requirements refer to a generally comprehensive methodology used by firms to calculate the probability distribution forecast (PDF). The internal model is thus not reduced to an instrument of arbitrary nature that already meets the requirements if all it does is, providing as output, a distribution of profits or losses with high forecast quality. Instead, besides the resulting PDF, the individual elements of the calculation methodology are subject to quality standards; these are mainly the underlying assumptions, the actuarial and statistical techniques used, and the data and information used as basis for model specification and parameterisation. This corresponds to the view that an internal