The Indian stock market is experiencing tremendous changes since the past few years. In the recent past, the market witnessed erratic fluctuations in stock prices. The unexpected shocks over time lead to ups and downs in the market and hence, large swings in price. This unpredictable change over time has to be measured as it represents the uncertainty and risk. The estimation of this unpredictable change, the so called volatility, is indispensable in any economy as it is an integral part of any investment or financial decisions such as asset allocations, derivative pricing or risk management. In this paper, we discuss different mathematical models to model the volatility of the stock market in general and apply it to Indian context to pin down one, that captures the irregular behavior of the Indian stock market.