Endogenizing Model Risk to Quantile Estimates

We quantify and endogenize the model risk associated with quantile estimates using a maximum entropy distribution (MED) as benchmark. Moment-based MEDs cannot have heavy tails, however generalized beta generated distributions have attractive properties for popular applications of quantiles. These are MEDs under three simple constraints on the parameters that explicitly control tail weight and peakness. Model risk arises because analysts are constrained to use a model distribution that is not the MED. Then the model's alpha quantile differs from the alpha quantile of the MED so the tail probability under the MED associated with the model's alpha quantile is not alpha, it is a random variable. Model risk is endogenized by parameterizing the uncertainty about this random variable, whence the model's alpha quantile becomes a generated random variable. To obtain a point model-risk-adjusted quantile, the generated distribution is used to adjust the model's alpha quantile for any systematic bias and uncertainty due to model risk. An illustration based on Value-at-Risk (VaR) computes a model-risk-adjusted VaR for risk capital reserves which encompass both portfolio and VaR model risk.