We investigate capital requirements based on Value at Risk (V@R) and Average Value at Risk (AV@R) when the bank's econometric model only approximately describes the true, unknown return generating process, as is often the case in practice. We provide a simple formula for such capital requirements that uses a first order Taylor expansion of V@R and AV@R around a model confidence parameter. This formula allows the bank to reflect the confidence of the econometric model into capital requirements in a theoretically consistent manner. We derive feasible upper bounds on the first order approximation of the true, unknown V@R and AV@R. An empirical application to daily S&P 500 returns shows that the upper bounds are tight and provide valuable information for assessing capital requirements in the presence of model risk.