Big banks are facing new allegations they conspired to control pricing and access in the lucrative credit derivatives markets.

Three Danish pension funds and their investment-management company filed a lawsuit Thursday in U.S. District Court for the Northern District of Illinois, alleging antitrust violations and saying the banks "unreasonably restrained competition" in the $25 trillion credit-default-swaps market. The funds allege that the harm done to investors as a result of anticompetitive practices was "in...