If the amount is really large, then you owe it to yourself to do some research.
My gf frequently converts $10k worth of JPY into USD, which isn't large enough to deal with currency houses in NY, but sufficient to get a slightly better rate from Wells Fargo (though still 200+ basis points away from the WSJ rate).
The local WF branches hate it when we do this because their managers claim that the difference gets billed to them.
Recently, I've been migrating her over to buying dollar coins with her credit card. Buying those gets her very close to the spot rate plus JL miles. Do you happen to have any CCs in Saudi Arabia that don't charge premiums for foreign purchases?