The provisions outlined are relevant for our institution and we intend to model a volatility surfaces and curves across a variety of asset classes with parametric functions.
We have a preference for OPTION 2. The requirement for two calibrations in OPTION 1 leads to a more complex implementation. For some combinations of modellable and non-modellable buckets the parameter calibration may not even be possible with OPTION 1 (see the response to Q9).We request feedback on whether the following interpretation of OPTION 2 is acceptable:
When we use parametric function parameters as risk factors in the internal risk-measurement model, two aspects of this choice are important:
a. The risk-measurement model will use perturbations to these parameters to measure portfolio risk. A single perturbation will produce a single P&L result.
b. Perturbations to parameters can be converted into equivalent perturbations to each of the points in the curve, surface, or cube where were used to calibrate the function parameters.
To determine the modellable or non-modellable P&L from a single parameter perturbation, we require an appropriate methodology to allocate the P&L to modellable and non-modellable buckets. The ES calculation then consists of perturbing the parameters using ES shocks and calculating the P&L due to modellable points on the curve, surface, or cube. In a similar fashion, the SES calculation consists of perturbing the parameters using SES shocks and calculating the P&L due to non-modellable points on the curve, surface, or cube.
OPTION 1 could result in a requirement to fit a parametric model with an incomplete data set. As an example, if the parametric model has three parameters, but fewer than three data inputs belong to modellable buckets, then a set of possible calibrations are possible. The parameter fitting methodology would require a heuristic for picking a single calibration from this set which adds extra complexity to the parametric model specification and validation.