What analysis has been done to predict the next big financial crash?
A useful principle to have in mind here is the so called 'volatility paradox´ oft-cited by Marcus Brunnermier (Princeton prof):

The idea is as follows: a) financial institutions are in the business of taking reasonable risks; b) when the financial system is deemed very stable, then it makes sense for financial institutions to engage in risky activities, because, if the system is stable those risky bets are manageable, reasonable bet; c) when all financial institutions jointly engage in risky activities, the system becomes unstable. In other words, safety engenders individual risk-taking, which creates aggregate risk. This works the other way too: riskiness engenders risk averse attitudes, which lead to a stable system.

If you believe this story then you get some insight into why its difficult to predict crises: they happen when risks build up during periods of safety and stability...