Analytical solutions are available only for relatively simple systems. Symptoms with multiple interactions and nonlinear equations often can't be solved analytically. Computer models are simply approximate solutions to differential equations. If an analytical solution is available it is always preferred. If you don't include an equation covering a certain variable then your model can't possibly predict it's impact. The complexity of climate models challenges the capabilities of even our best computers. We are not at a point where anyone can expect models to be perfect.

It is also unreasonable to wait until they are when models that we do have show potentially severe consequences. The models you referred to were based on no data quite unlike climate models which have been tested against hundreds and thousands of years of data. Derivatives are only about a decade old and models would not be challenged untill housing prices started to collapse. Frankly, since the profit motive was involved with these models they are yet another example of corporations believing what makes them money rather than what common sense should tell them. Making more risky loans should increase risk just like increasing a greenhouse gas should warm an atmosphere.

The fact is many researchers have built different models including different secondary factors that yield similar results. That could be because they fit the same data set or that the most obvious equations to include are the most important ones. I would hope they determined the coefficients in their equations through experimentation or evaluation of data with only one key variable, but it is possible they are simply doing a polynomial style fit. Even if it's the later that method is used in the real world to make engineering and business decisions where the issues aren't high profile political footballs.

Regards,
Mark