Lots of fun!

My first job involved writing option models, so I knew Black-Scholes intimately. 20 years later, I was sitting in a hotel in Mountain View waiting for a car, and I picked up an article in some reputable newspaper saying, "Black-Scholes is broken!"

I laughed and said, "This will be something fun I could refute in a few moments while waiting for this car." I started reading and about two minutes into it I jumped up. "Shit!"

The issue is simple.

Black-Scholes is perfectly correct if traders were roughly split between being long volatility and short volatility. But in fact, Wall Street tends to sell volatility, by writing options and selling them to clients, so Wall Street as a whole is heavily short volatility.

That means when the market moves a lot in one direction, all the traders are going to be delta-hedging at the same time in the same direction, which spoils the "unbiased lattice" property (as likely to go up as down) that Black-Scholes depends on.

The worst is that this explains a lot of catastrophes that had happened in Wall Street while I was there, and it should've been obvious to us, but it wasn't.

Thanks for a great article, and one that brought me back to my sinful past as an investment banker. My only excuse is that I was young and stupid, but I would not do that again, but it was a lot of fun for a young person.

(Oh, the "Chaos Theory" example is I believe sorta bogus, as it was in the original book you are writing about. That recurrence relation is an example of one that produces chaotic behavior, or at least so I think, but there are many others. It could be I am wrong, though, I was never an expert and haven't touched this field in a long time.)