ZURICH (Reuters) - Swiss Re (SREN.VX) expects natural catastrophe pricing rates to stabilize in 2014 after a decline this year, with demand for the cover doubling by 2020 in high-growth markets.

The Swiss reinsurer, which helps insurers shoulder risks in exchange for part of the profit, said on Monday its business model was not challenged by increased competition from alternative sources of capital for the insurance industry.

Reinsurers have seen their pricing power diminish and their relevance threatened as investment funds seeking higher yields have funneled billions of dollars into so-called "catastrophe bonds" sold by insurers to share the risk they take on for natural disasters.

"We take the inflow of alternative capital seriously, but we are not alarmed by it," said Swiss Re's chief underwriting officer Matthias Weber. "Smaller, less diversified reinsurers, however, will be under significant pressure."

Around 70 percent of this alternative capital targets U.S. natural catastrophe risks, while other business units are less affected, the reinsurer said ahead of a news conference at the annual meeting of the reinsurance industry in Monaco.

Swiss Re, which competes with Munich Re (MUV2.DE) and Hannover Re (HNR1.DE), said the liability insurance market in the United States is firming, while price trends are expected to remain stable in other property and casualty units.

(Reporting by Alice Baghdjian; Editing by Mark Potter)