The paper studies the empirical relationship between Oil Price Shocks and Stock Market Index movement and their asymmetric responses to oil price shocks. The Indian stock market index was represented by Sensex, and daily closing prices of Sensex and crude oil prices for a ten-year period between 2006 and 2015 wereanalyzed using dynamic linear regression or ARIMAX. The study indicated that there is no significant evidence of correlation between oil price shocks and stock market index movement; however, stock market index movement is auto-correlated with its two lags. The findings of this paper also show statistically significant asymmetric responses of stock market index movement to oil price shocks. Stock market index movement was negatively correlated with positive oil price shocks, and positively correlated with negative oil price shocks. Subsequently, the equations of the models are used to forecast the stock market index movement. This study uniquely enhances the understanding of bivariate relationships