Journal of Risk Model Validation

What can we expect from a good margin model? Observations from whole-distribution tests of risk-based initial margin models

David Murphy

  • It is possible to derive predictions of the future distribution of portfolio returns for popular classes of risk-based initial margin models.
  • These predictions can be used to test margin models by comparing them with actual returns. The resulting test is higher power than typical back-testing approaches. It can also be used for model calibration/sensitivity analysis.
  • The results of applying a whole distribution test to popular initial margin models suggests that it is relatively straightforward to design and calibrate a model which performs well slightly beyond the typical confidence intervals required by regulation, 99% and 99.5%.
  • Different models vary substantially in their reaction to high stress, and no model fits the far tail well. This suggests that stress testing, such as that used to sized central counterparty default funds, is an important adjunct to risk-based margin estimation.

Initial margin is typically calculated by applying a risk-sensitive model to a portfolio of derivatives with a counterparty. This paper presents an approach to testing initial margin models based on their predictions of the whole future distribution of returns of the relevant portfolio. This testing methodology is substantially more powerful than the usual “backtesting” approach based on returns in excess of margin estimates. The approach presented also provides a methodology for calibrating margin models via the examination of how test results vary as the model parameters change. We present the results of testing some popular classes of initial margin models for various calibrations. These give some insight into what it is reasonable to expect from an initial margin model. In particular, we find that margin models meet regulators’ expectations that they are accurate around the 99th and 99.5th percentile of returns, but that they do not, for the examples studied, accurately model the far tails. Moreover, different models, all of which meet regulatory expectations, are shown to provide substantially different margin estimates in the far tails. The policy implications of these findings are discussed.

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