• Hong Kong has witnessed more than nine months of protests.
  • A rally on Sunday again turned violent.
  • Trading fees at the bourses skidded 10% in the third quarter of 2019.

The Chinese government should and will let authorities in Hong Kong resolve the continued public protests that have beset the financial center, according to the chair of the Hong Kong Stock Exchange (HKEX).

Hong Kong has witnessed more than nine months of protests over a now suspended extradition bill that would have allowed people in the city to be sent to the mainland for trial. The public disorder has spread to consider other issues such as rampant property prices. The most recent rally on Sunday once again turned violent.

Speaking to CNBC's Geoff Cutmore at the World Economic Forum in Davos on Monday, the chair of the Hong Kong Stock Exchange, Laura Cha, said she felt Beijing would resist from interfering.

"I believe that it will, and it should. It is a local issue under one country, two systems," said Cha.

For 10 years until 2018, Cha was a member of China's National People's Congress, acting as the Hong Kong deputy. The businesswoman added she believed that Hong Kong would soon be able to tackle the issues that have led to the unrest.

Laura Cha, chairman of Hong Kong Exchanges and Clearing Ltd., speaks at the World Federation of Exchanges (WFE) General Assembly & Annual Meeting in Singapore, on Wednesday, Oct. 9, 2019. The annual meeting is where leaders of global exchanges, regulatory authorities, industry experts from academia and the media gather together for in-depth discussion on major issues surrounding the exchange industry. Photographer: Ore Huiying/Bloomberg via Getty Images

"We should be able to resolve the issues and the (Hong Kong) government are beginning to resolve some of the issues."

Cha said because of the protests, the HKEX did suffer a hit to trading volume throughout several months of 2019 but that had rebounded "quite nicely" in recent weeks.

This year, the Hong Kong government has increased the size of its delegation to the annual talk-fest at Davos. Cha said Hong Kong has realized that it needs to get its story out and persuade people that it was open for business.

"Yes, there are arrests. Yes, (there is) what you see on television. But there is another side of it. The financial market has done well. The capital market is still very strong," she said, adding that there had been no significant outflows of capital.

"All this points to the fact that global investors still see us as an attractive market. There are obviously signs of concern, but we hope the concerns can be resolved soon," she said.