This paper aims to explore links between the Indian stock market and three developed Asian markets (i.e. Hong Kong, Japan and Singapore) using cointegration methodologies in order to explore interdependence. We further estimate the time-varying conditional correlation relationships among these markets. We find that correlations rose dramatically during periods of crisis and return to their initial levels after the crisis. Finally, we investigated the presence of different volatility regime across stock markets. International investors may find useful to model their portfolio by also considering how volatile stock markets are. Results show that estimated probability of being in the low volatility state is the highest for all stock markets considered, as well as the probability to switch from a medium- to high-volatility state. Results suggest a short-run relationship and absence of a strong long-run relationship among these markets. Absence of long-run linkages among these markets may provide potential benefits for the investors that look at emerging markets to enhance their risk adjusted returns by including emerging markets in their portfolios.