The Black–Scholes formula revolutionized option markets by providing a fair price for European-style options. This led to the rapid expansion of option markets, making them highly liquid and diverse. The formula, rooted in complex financial and mathematical theories, elegantly captures the tension between time decay and convexity in options. It assumes a lognormal distribution for stock prices, simplifying predictions. The formula’s assumption of no arbitrage reflects a noise-free, coherent market where prices are consistent. Understanding this assumption reveals the essence of option pricing. The formula’s beauty lies in its ability to provide the platonic price in an idealized world of risk neutrality.
https://gregorygundersen.com/blog/2024/09/28/black-scholes/