They don't literally have the prize money sitting in a bank account. What they do have is legally binding contracts with people that say "When you determine a prize winner, we'll give you the money to pay out the amount you've promised." (James Randi's prize for demonstrating psychic powers under controlled conditions is funded the same way.)

which is currently unproductively sitting in a bank account.

And the reason for that is that this money is dedicated to the prize and cannot be touched until and unless the prize gets awarded.

Which, I think, is the standard way these things get done. Otherwise you'd get into situations where you spend the prize money on "administering" the prize, but when the time to actually give out the prize comes... oh-oh, where did the money go?