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The most common derivation of Black-Scholes absolutely does assume a standard normal distribution. There are other models that don't (i.e., Mandelbrot tried to
by jfager 14y ago
The most common derivation of Black-Scholes absolutely does assume a standard normal distribution. There are other models that don't (i.e., Mandelbrot tried to get people to use Levy distributions, and a lot of newer models are built around martingale theory), and traders have adopted rules-of-thumb that pull prices out of line with what BS says they should be, but it's certainly not the case that anyone who speaks of BS assuming Gaussians is lying or speaking from ignorance.
- omonra 14y agoUggh, no. Let me try and explain. BS is not used as a model that explains how the world works. It's just a formula to convert volatility to a dollar price of an option. But the actual vol surface that people use is anything but Gaussian. So the job of the trader is to construct a vol surface. However in order for 2 people to trade an option, they have to agree to a cash price - which is when BS is used. But the entire trading universe revolves around vol surfaces. Think of it as making a painting. BS is just a single paint pigment - whereas the painter will take 20 pigments and mix them up to produce millions of colours. So to accuse those who use BS formula of assuming Gaussian probability distribution is akin to saying that painters use one color to paint.