Economists fell for the myth of Black–Scholes. This is a neat way of quantifying risk, but it assumes that risk has a Gaussian distribution. Sometimes it doesn't.
Economists fell for the myth of Black–Scholes. This is a neat way of quantifying risk, but it assumes that risk has a Gaussian distribution. Sometimes it doesn't.
Maybe you're being loose with your terminology, but there is no such assumption. The simplest versions of Black-Scholes does assume that stock price is a lognormal process with constant variance/volatility, which empirically it isn't.
The point of Black-Scholes is to price derivatives not quantify risk, but the price also has an empirical market price. Just as you can use the 'assumed' variance/volatility to try to compute the derivative price (according to B-S), you can use the market price of the derivative to compute the 'implied' variance/volatility.
If you look at the options page for AAPL on yahoo finance[0], you'll see a column for implied volatility, the above method is precisely how it is calculated.