If markets are irrational, you can become extremely rich by exploiting markets' biases.

Black-Scholes and other quantitative approaches are used to price options and other derivatives.

Your question mentions derivatives (including options, futures, swaps and more). It seems to refer to credit default swaps. And then makes a blanket statement about irrationality.

I suggest that you start with a simple textbook on derivatives like Hull and learn the terminology plus basic derivatives math so you can reformulate your question more precisely so it is possible to give you a better answer.