Journal of Risk Model Validation

Quantification of the estimation risk inherent in loss distribution approach models

Kevin Panman, Liesl van Biljon, L.J. Haasbroek, Willem Daniël Schutte and Tanja Verster

  • A generic methodology for quantifying model risk, and more specifically estimation risk, is proposed.
  • The choice of sample size, distribution tail heaviness and percentile to be estimated all have a material impact on the quantum of estimation risk.
  •  Aggregate estimation risk across a portfolio of models reduces materially – similar to a diversification benefit.
  • Extreme quantiles are more likely to be over-estimated than under-estimated.
  • Model-error over-estimation is unbounded.

Financial institutions rely heavily on risk models for operational and strategic purposes. These models are simplified representations of complex dynamics and are therefore prone to contain a quantum of “model risk”. Although model risk management practices have materially improved in recent years, model risk quantification approaches, which can assist in further advancing model risk management, require more development. We propose a generic approach to quantifying the estimation risk of risk models using the error of a maximum likelihood estimator. We label our approach “simulate errors from assumed truth”, or SEAT. To demonstrate SEAT, operational risk examples using the loss distribution approach (LDA) are examined. The simulation design is chosen to include sparse loss data and heavy-tailed severity distributions. Model risk exposure is materially reduced when loss data samples are larger, the severity distribution exhibits light tails and the model is used for less-extreme quantiles of the aggregate loss distribution. In fact, model risk is reduced by up to 75% when the target percentile is lowered from the 99.9th to the 95th percentile for practical heavy-tailed distributions. Further, the aggregate model risk across a portfolio of risk models is much smaller than that of the individual risk models – a reduction of 29.5% in some of our examples. Finally, we show that a firm is more likely to overestimate than underestimate capital requirements calculated from extreme quantiles in our example.

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