The heck with finance and their math models. Let's look for an answer to the banks' foulup in quantum physics: Schrodinger's bank.
Put a bank in a box (obviously, a safety deposit box). The bank fails (all equity is lost, executives are beheaded) with p=.5 or is saved (Treasury buys junk) with p=.5
Actually, this uncertainty might be the problem now; credit is frozen because nobody knows who to trust.
But the Paulson plan seems to assume we should now try and save everybody. Why? Maybe we just need clarity on who is saved and who is damned [Lehman employees: insert "why me?" rant here]
Example using the classic cat
http://www.phobe.com/s_cat/s_cat.html or an explanation involving reincarnation here.
Unlike the cat, banks and the FDIC get to choose whether to go into the box.
(Ordinarily, the bank gets to choose, but if certain criteria aren't met, the FDIC can force the issue.)