In MTW I you can borrow money if you have no cash to ransom back your prisoners, the only occassion where you can go into debt actively (the other way is running up such a large payroll bill that your income can´t handle it, of course, which still works in RTW - I don´t know about MIITW).

In reality, the decision wasn't one of "pay the ransom now or we execute instantly" - it wasn't uncommon for captured nobles and royalty to be held for years on end until their families could afford the ransom.
Yep, remember Richard Lionheart, or the Duke of Orleans after the battle of Agincourt, it took about fifteen years before the latter was exchanged for the Earl of Somerset (who was a prisoner for almost as long), and one of Henry V´s claims that refuelled the Hundred Years War in 1419 was the still unpaid ransom for King Jean, long since deceased at the time.