One reason why banks and other financial institutions committed so much to trading derivatives was because they had models that told them that their investments were sound. This all turned out to be false.
The attached article is a challenge, but illustrates the problem of assumptions and abstracting. The Black-Scholes equation was the first equation which valued investment options in a seemingly reliable way. It worked for a long time and encouraged the use of similar mathematical models that valued more complex assets in what were essentially gambles.
Regardless of what we may think of banks gambling with their clients money, the way these valuation models worked is fascinating. The bankers made assumptions on volatility and various other variables and the models became more ambitious. It turned out that the models did not survive reality with disastrous results. Yet it was quite clear that the models could never survive reality to anyone outside the financial sector.
The article is excellent reading for all those interested in financial economics and doing economics at university.
Although I do see the enormous potential of mathematical formulae in the investment market I still see one fundamental flaw - humans do not act rationally. Equations can get you a very long way looking at statistics, derivatives, price fluctuations etc and although most investors will do all that they can to gamble on the right direction they are gambling on normal human beings. The derivatives that are be traded could be as simple as someone paying back their mortgage but what if this person opens up the account as a highly paid lawyer but under their irrational human nature quits their job a week later to pursue their dreams as a human rights activist and never earns a penny for the rest of their lives. They will never pay back the debt. Mathematics cannot judge people's behaviour so equations like the Black-Scholes formula are always going to have limitations and a more obvious flaw was pointed out in the GFC as to be accurate formulae must be tailored to the market so as the market changes the formulae must also be adapted.
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