The two schemes are the Qualified Foreign Institutional Investor (QFII) scheme and its yuan-denominated sibling RQFII.
China has continued to open up its financial markets to foreign investors, despite ongoing trade tensions with the United States and the coronavirus outbreak, to provide much-needed capital for its economy.
As of September, overseas individuals and institutions held a total of 2.75 trillion yuan ($18.43 trillion) worth of Chinese equities, according to data from the country's central bank.
The inclusion of Chinese stocks into international indexes provided by MSCI, FTSE Russell and S&P has increased the urgency of further deregulating the derivative market, because foreign investors have long complained about a lack of hedging tools in China.
China imposed draconian restrictions on stock index trading during its stock market crash in the summer of 2015, sharply raising margin requirements and tightening position limits.
Although it has been gradually loosening those restrictions, investors have complained current rules are still too rigid.
Stock index futures trading turnover on CFFE reached 1.1 billion yuan in September, only about a tenth of that in June 2015, when China's stock market crash began.
Currently, there are three types of stock index futures traded on CFFE - CSI300 index futures, CSI500 index futures and SSE50 index futures.
($1 = 0.1492 Chinese yuan renminbi)
(Reporting by Luoyan Liu, Andrew Galbraith and the Beijing Newsroom; editing by John Stonestreet and Mark Potter)