In this thesis, we introduce the methodology for estimating and evaluating parametric and non parametric VaR. A commonly used methodology for estimating market risk that has been endorsed by regulators and financial industry advisory groups is value-at-risk(VaR) which is defined as the absolute value of the worse loss return not to be exceeded with a probability of at least ?. Despite the increased use of the VaR methodology, it dose have well-known draw-backs. VaR is not a coherent risk measure and does not give any indication of the risk beyond the quantile. Beder has empirically demonstrated how different VaR models can lead to dramatically different VaR estimates. The standard VaR computation require that underlying return generating processes for the asset of interest be normally distributed, where the moments are time invariant and can be estimated with historical data. Neftci point out that extreme event are structurally different from the return generating process under normal market conditions. VaR is in fact the quantile of loss distribution for an asset. Consequently, the non parametric approach of VaR estimation is indeed the estimation of the loss distribution. The kernel estimator is the basic methodology employed to estimate the density. Several studies find that the return volatility of stocks tends to exhibit long-range dependence, heavy tails and volatility clustering, so that self-similar processes be employed to capture these characteristics in return volatility modeling. In linear regression analysis, a standard assumption is that variance of all squared error tem is the same. This assumption is called homoskedasticity. However, many time series data exhibit hetroskedasticity, where the variance of the error terms are not equal andin which the error term may be expected to be larger for some observations or periods of the data than for others. Autoregressive conditionally hetroscedastic (ARCH) models were introduced by Engle (1986) and their GARCH (generalized ARCH) extension is due to Bollerslev (1989). In these models the key concept is the conditional variance, that is, variance conditional on the past. ARCH model is useful in finance to model return variance or volatility of major asset classes including equity, fixed income and foreign exchange. In parametric approach using an ARMA-GARCH modeled using the normal distribution, fractional Gaussian noise, fractional Levy stable noise and Levy stable distribution and we compare performance of VaR models based data at 1-day level for the S am500 index. In this thesis we propose an approach for calculating VaR that utilize the ARMA-GARCH model with Levy stable processes. Although the student-t , skewed-t distribution can account for heavy tail, the memory effect cannot be neglected for these data. The Levy stable processes can capture both the heavy tailed and memory effect observed in the data.