Robust capital requirements with model risk

We study capital requirements when the bank's econometric model only approximately describes the dynamics of portfolio returns—which is virtually always the case in practice. We derive a simple formula for capital requirements based on a first-order Taylor expansion of the Value at Risk around a ‘model confidence’ parameter. This formula allows to reflect the bank's confidence in the econometric model into capital requirements in a theoretically consistent manner. Numerical and empirical applications show that our formula provides valuable information for quantifying capital requirements under model risk