A couple of months ago my son pointed me towards a product sold by Home Depot which works very well. It's called, "Hot Shot - Home Insect", clear formula for use indoors and outdoors. Kills roaches, ants, spiders, and other insects. Comes in a 32-oz spray bottle. No odor, non-staining.
It is, of course, toxic. People and pets should not be allowed in sprayed areas until it dries.
I've used it on my sailboat in a marina which has to be the mother of all spider-generators. Most aggressive beasts I've ever seen. This stuff kills em, along with other insects. Works well for weeks until it gets washed off.