To put up a security light do I need to install a box or can I just mount it to my house as long as the wires don't touch?

All permanent fixtures (such as lights) must be mounted on an appropriate electrical box.

Some "security" light fixtures are designed to be mounted directly to the building, and not to an outlet box. See photo.

The splices should be in a box. Either cord rated for wet location or UF cable will come out from the bottom of the arm, and can continue into the building, or stop at a junction box on the building and splice to the building wiring.

There is nothing wrong with splicing wiring in mid air on the exterior of a builidng, but a better job would be to enclose the splices in a box.