Abstract: Proof that under constraints of Put-Call Parity, the probability measure for the valuation of a European option is risk neutral under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets. The heuristics used by traders for centuries are both more robust and more rigorous than held in the economics literature.
I’ve recently read the book Antifragile: Things That Gain From Disorder by Nassim Nicholas Taleb. It’s obviously not a diet book, but the principles in it are highly relevant to weight loss.
But first, a bit of background. We are all familiar with things that are fragile. If you drop a Ming vase from a height, it shatters. Something that is resilient on the other hand, when dropped from a height withstands stress. An example might be an iron bar.
But until now, we didn’t really have a word for something that gets stronger when it’s placed under stress. That’s why Mr Taleb coined the term “antifragile”.
A good example of antifragility is the system of airline safety. Notwithstanding a few recent tragic examples, air travel gets safer and safer every year. The reason being that every time there is a crash, the incident is scrutinised, causes are elucidated and then measures are taken to try and avoid it happening again. Every air crash makes the next one less likely.
In other words, the system is set up to respond positively to negative things. Every bad incident makes the overall system stronger.