So cool to see it.
This formula provides an answer to the question "What is the chance that two members of the same pool will default on their loans?"
The point of the equation is to calculate the probability that A and B both default in our time period. Investors used this equation to choose investments A and B so that this probability that they both default is as small as possible.
Most of the magic seems to lie in two places:
- The probability distributions (the F variables), which describe how long each investment is likely to survive.
- The correlation parameter (gamma), which describes how the two investment survival probabilities rise or fall together.
Anyway, it is interesting to see the actual formula. It feeds into my scepticism about people trying to push epistemological limits. Maybe we can't solve everything with equations. Just because you can associate a number with it, doesn't mean the number really has any meaning. These quantitative masters of finance thought they could control risk by associating formulas and numbers with everything, but ultimately risks can't be controlled by numbers.