i dont know about india, but i would agree with you on one thing "You are living in the best city in the world".
There are several things to be done as i said, for starters you would need a license/ permission for starting a stock exchange from SEC and other regulatory authorities in US.
Second you need to set up the data center with the price matching software running on for five days a week, with high speed connections, or may be a separate dedicated line would be a better choice as any down time below 99.8% would itself kill the whole project.
Third you would have to partner up with banks and other financial institutions to trade on your platform. Like actually use it. cause you need the trade volumes to be managed and should be above a certain point, which means you need to manage a few hundred thousand transaction transactions per second.
These are just three top of my head, and this is just like a grain of sand in the desert there are several other thing which would take me whole night to describe but if you want to know it in a more detailed way, like if you are actually crazy
enough to peruse the idea, feel free to send me an email at (mohtashim_ansari@live.in) i will be glad to help.