Many of the techniques used in calculating VaR rely on simulations that can be difficult and time consuming. One of the objectives of this paper is to conduct statistical inference for VaR based on saddle point approximation and volatility estimation. Specifically, by assuming that the loss distribution is a generalized hyperbolic, we propose a quasi-residual based volatility estimate. Because saddle point approximation furnishes a fast and accurate means to approximate the loss distribution and its percentiles, including the VaR in particular, it is then used to approximate the loss distribution of the quasi-residuals from which VaR can be estimated. Simulation studies and data analysis confirm that the proposed methodology works well both in theory and practice.(volume 20, number 3)