A valve assembly is installed within a wellhead such as a conventional tubing hanger or casing hanger used to suspend pipe or other tubular goods in a well. A seal bushing assembly is installed in a tubing head assembly or other wellhead component. A hanger valve assembly is stung into the seal bushing assembly and includes a valve that can be selectively opened or closed. In the open position, the valve does not restrict a central flow path diameter through the hanger and wellhead. In the closed position, the valve contains pressure and/or fluid flow and fully seals against wellbore pressure acting on the valve. A wellhead adapter covers the hanger valve assembly and provides an attachment point for a conventional Christmas tree or other wellhead equipment.