I think the key property of copulae that will interest intelligent senior management is that you estimate the chance of two or more unlikely events happening at once from their individual chances of occuring rather than from patterns of common events. The example I like to give is suppose we wrote someone an insurance policy that pays $1 million if they get a hole in one at the golf course and are hit by lightning just as the ball drops into the cup.
It's never happened before (I assume) so we can't use direct historical data. There's no really good, reliable way of pricing the policy.
Copulae look at the total numbers of holes in one and the total number of people hit by lightning on golf courses, then makes some simple, reasonable assumption about overlap. There's guesswork involved, but you're looking at the right data.
Standard analysis will look at the correlation between golf scores and rainfall. This is silly, you're not looking at the events of interest. Although the analysis will appear more precise, it cannot possibly be right because it doesn't have the right data.
