How Black & Scholes is used

If you had an uncalibrated weighing machine do you use it to find “the true weight” or do you use to “find if you are losing weight and if your friends are heavier than you”?

Surely you would use it only to compare weights or how the weight has changed. Because the machine is uncalibrated it cannot be used to find the true weight.

Black & Scholes is an uncalibrated instrument that can tell the fair price of an option. It is uncalibrated because the market doesn’t always move in a geometric Brownian motion.

So people use it to compare prices of options or the price of the same option under different market conditions.

The various Greeks show how sensitive the price of an option is to various market conditions like directional movements (delta), days to expiry (theta), volatility (Vega). Gamma shows how erratic the price of an option is as the underlying moves around.

Even these sensitivities are only accurate in the intuitive sense because in a trending market (autocorrelation) geometric Brownian motion is not followed the black and Scholes misestimates everything.

One of the main other uses of Black and Scholes is to calculate what the volatility would have been had everyone used Black and Scholes and had the prices moved in a geometric Brownian motion. This is possible because every other parameter of Black and Scholes model is known to all market participants. All that is unknown is how much volatility does everyone expect when pricing their options. Again here we have not concerned with the numerical volatility everyone expects. We are only concerned about how everyone ranks against each other and over time in terms of future volatility they expect. This is why implied volatility rank is more important than the true volatility.

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