Ammo, not in a gun, pops like popcorn. Even large quantities of smokeless powders just burn very energetically. They do not explode. Think about a road flare compared to a bomb, same amount of energy released, but the shorter the time frame, the greater the issue. A five gallon can of gas, or several grill size propane tanks, in a garage, are more of a concern to a fire fighter.
Hollywood special effects often do not mimic real life. If you think about ammo and physics you have a loaded shell with a very heavy lead end and a lighter brass end. When the powder cooks off force is exerted in every direction. In a chamber the bullet is forced down the bore because that is the only open direction. Outside the chamber forces are not contained but you have a very heavy bullet on one direction and a much lighter brass case in the other, so the lead bullet becomes something the brass case pushes against. The bullet remains almost motionless and the brass flies in the other direction, until the gases dissipate, as soon as they lose containment. You get a flare, but no supersonic projectiles going through wall to reek havoc. You do get a pop from the primer as well. If you want to have some fun load a few shells with spent primers and toss them into a fire. You wont get the pop or bang you expect. Now as our President has pointed out, not all bullets and shells are created equally. I shudder to think about the organ, eviscerating, dangers, of all my stored .410 ammo.
Some homeowners policies have limits about how much powder you can have in your house. Also a few state do limit the quanity of powder you can store in your house. Check you local and state regulations and insurance policy.
