Under liberalized remittance scheme of RBI, resident Indians are allowed to remit upto USD 75,000 in a financial year to invest into stocks. Check this link, RBI allows you to invest, but you cannot trade on any product which might have margin or margin calls (basically any leveraged product like F&O) using this money that you have remitted abroad.
There are a couple of banks who also run brokerages who offer overseas trading account for you to invest into international stocks (note that presently these platforms let you trade mostly stocks listed on the US stock exchanges).
So yeah, you can can open an overseas trading account and get started.
If your view is not on a stock, but on the entire market, there is F&O on a bunch of indices that trade on NSE and BSE, it will be a lot more easier to take a position in them than to open an overseas trading account. Some of the international indices that trade on NSE/BSE are:
| Country | Index | Exchange |
|---|---|---|
| USA | S&P 500 | NSE |
| USA | DJIA | NSE |
| UK | FTSE | BSE |
| Hongkong | Hangseng | BSE |
| Russia | Micex | BSE |
| Brazil | Bovespa | BSE |