Value at Risk, often referred to as VaR, is a commonly used risk measure in the financial industry. Value at Risk measures the maximum potential change in value of a portfolio of financial instruments with a given probability over a pre-set horizon. Statistically speaking, the VaR of a portfolio is the quantile of the distribution of that portfolio’s loss over a specifed time interval, at a given probability level. Despite many advantages of using VaR methodology (simple to understand, frequently available in various types of financial software), there are certain drawbacks - most importantly, it creates a false sense of security because Value at Risk does not measure worst case loss. One of the main goals of this graduate thesis is to describe Value at Risk approximating methods in conditional Gaussian class of models (i.e. the risk factors are assumed to be joint normal). The emphasis is being placed on Delta-Gamma approach where the assumption is that there is a reasonably good quadratic approximation (as a function of risk factors) of the change in the portfolio’s value. Our first method used to determine a quantile of the distribution of the change in the portfolio’s value is called Cornish-Fisher approximation. It is a relatively fast method that gives approximations with sufficient accuracy in many practical situations but it can be mediocre in worst-case scenarios. The second method that we examine is partial MonteCarlo method with importance sampling. Importance sampling method helps us generate more samples from the region that is more important for the problem at hand. Partial Monte-Carlo method is slower, but more accurate than Cornish-Fisher approximation. The second main goal of this graduate thesis is explaining the applications of copulas for the calculation of Value at Risk. Copulas are functions that can be used to describe the dependence between random variables with arbitrary marginal distributions. In the end we describe the procedure for computing VaR with copulas.