This paper makes an attempt to explain the procedure as well as estimate the VaR of a selected portfolio of the Nifty Sectoral Indices using approaches such as GJR GARCH-EVT-Copula, Filtered Historical Simulation, Generalised Extreme Value Theory and t Copula. The GJR GARCH-EVT-t Copula model extracts the filtered residuals obtained using the GJR GARCH technique and by using the Gaussian Kernel method for interior of the distribution and Extreme Value Theory for upper and lower tails to estimate the cumulative distribution of the residuals. A comparison is made between the estimated VaR simulation by the Monte-Carlo method, the aforementioned method and by using t Copula to get the joint distribution of each sectorial indices. The normalised maxima of the sequence is measured by the GEV distribution. An alternative to the Monte Carlo simulation and the Historical simulation is the FHS technique. The mean equation is modelled using the ARMA model while the volatility is modelled using GARCH with a non- parametric specification of the probability distribution of asset returns. The VaR estimates of the equally weighted portfolio of NIFTY Sectoral indices of 95% and 99% confidence intervals are backtested over a 2478-day estimation window.

Keywords : Value at Risk, NIFTY Sectorial Indices.