The paper presents an empirical application of Extreme Value Theory (EVT) in modeling extreme behavior of financial asset prices. EVT is a branch of statistics dealing with the extreme deviations from the mean of probability distributions. It is the theory behind modeling the maxima of a random variable. Market risk takes extreme form when certain events, which are assumed to be rare in the distribution of assets, cause severe changes in the valuation of the portfolio. These rare events usually lie in the tails of the return distribution of the assets. We model two different risk measures with three different return distributions and analyze the importance of extreme value distributions in underscoring the behavior of extreme market moves. The paper highlights that the high volatility of Indian stock market associated with higher returns is better captured through extreme value distributions rather than conventional distributions. Also, for all the stock indices, EVT help in modeling the market risk better than conventional distributions.