No ground wire, no box (old or new) trying to install light fixture
You'll need a metal old work box with a BX/AC connector and insulating bushing

Your wiring appears to be BX (old style armored cable).  While the armor on BX is not up to modern standards as a grounding path, it's better than nothing whatsoever, and should be bonded to in any case.  This is done by using an appropriate armored cable connector fitted into a knockout on your new box -- this connector in turn uses a setscrew or spring clamp to retain the cable armor in the connector.

From there, you can ground the light fixture to the box using a grounding pigtail and screw into a 10-32 tapped hole on the back of the box, provided you get the correct box of course.  It will need to be a metal box (no plastic here!) with old work mounting means that attach to the existing interior sheathing materials (instead of being attached to a stud).