The purpose of this study is to know that how the National and International market, namely (S&P BSE SENSEX) (NASDAQ) (SSE) (FTSE) can influence the volatility of (S&P BSE BANKEX) return in India and the factors affecting the volatility for the same. However, the previous studies mostly considered the volatility of stock in the Indian capital market. But the present study mainly focuses on the Bankex return volatility. Here the researcher identified and estimated the mean and variance components of the daily Bankex return using Garch (1, 1) model by explaining the volatility structure of the residuals obtained under the best-suited model for the used data series. The method ML -ARCH (Marquardt) -Normal distribution has satisfied the criterion of model selection based on the three assumptions. These Null Hypotheses deals with the problems firstly, no serial correlation, secondly, the presence of no ARCH effect, thirdly, residual are normally distributed. We have chosen daily data period from 03 rd May, 2012 to 08th January 2016, nearly 914 working days of all markets for estimating Arch-Garch model. The study shows the significant result of ARCH and GARCH effect. The Bankex Return is also significantly affected by endogenous variable (SENSEX return). The NASDAQ composite and SSE composite Index are also statistically significant, In sum-up, the foreign market return volatility or outside shock can influence the volatility of BANKEX return. However, the FTSE 100 was not found statistically significant, revealing that volatility in FTSE return cannot transmit to S&P BSE BANKEX return in India.