[wavemode]

Sure, but isn't most of supply and demand in the market driven by large investors who use such formulas to derive the fair price of the option?

That is, if the real price ever differred significantly from what Black-Scholes predicts, wouldn't algorithmic trading very quickly correct this deviation?

[onerandompotato]

If there was a way to directly formulate every parameter of the black Scholes formula you would be correct. The problem that you run into is how to calculate volatility itself? Without the volatility value, your algorithm cannot trade on it.

Using history of volatility is insufficient, because volatility is a forward looking measure. Just because the stock was volatile in the past does not mean it will be in the future, and vice versa. There are even more nuances with this, as volatility is a smile (or a surface), not a singular number https://en.wikipedia.org/wiki/Volatility_smile.

TLDR Trading in volatility is a very complicated topic. However, volatility is a useful parameter, and black Scholes is typically used to deduce the forward looking volatility from option price, in addition to volatility -> option price.

[thaumasiotes]

> There are even more nuances with this, as volatility is a smile (or a surface), not a singular number https://en.wikipedia.org/wiki/Volatility_smile.

That article says that implied volatility is inconsistent, with options at strike prices that are very far from the current market price having costs that imply a different level of volatility than options at strike prices that are close to the current price. The cute question here is "should an option be priced according to the actual level of volatility in the price of the underlying asset, or should it be priced according to the level of volatility that exercising the option would require?"

Volatility is just a quantity.

[FabHK]

In a sense, BS and the option market enable trading in volatility itself.

Specifically, you trade in the estimate of the stock's volatility over the time from now to expiry of the option.

If you don't want to trade options directly to do that (it is cumbersome, as it involves "continuous" delta hedging), you can trade in VIX futures for the same purpose. Or variance swaps.