Slightly wonky topic today, but one that is very important. Most of you out there doing financial modelling should already know this (but could do with some reminding) and those looking into this sort of modelling (and bank management who get fed these reports) should know.
For most situations the normal distribution is not the one you should be using for financial modelling.
I’ll say it again in a different way – if you are going to use the normal distribution first prove that it is the correct one to use.
I know that the Basel II Accord mandates its use (even helpfully giving the Excel function “NORMSDIST” in the footnotes) as do many other regulations but there is a mountain of analysis in the academic sphere showing that the normal distribution is not the most correct – understating the probability of the “long tail” or “black swan” events.
Lévy distributions are much more correct – there are particular examples that give much more weight to the long tail than a typical normal distribution does. Work done by Mandelbrot and Taylor (yes, Mandelbrot of the pretty fractal pictures) in the 1960s first showed this and there has been considerable work since then. Just have a wander through Google Scholar for some fascinating reading.
Why then do we keep using the normal distribution? I think that it is just a habit and that we get it drummed into us at university. There has been an enormous amount of work done on the normal distributions, so we also look to leverage off this.
My message to management, then, is this – if a risk assessment comes to you having used the normal distribution the first question you should ask is “Why have you used the normal distribution?” If the answer is something along the lines of “We always use it.” then you should ask them to go back and justify its use. If the answer is “We have been told to do so by the regulators.” then you should tell them “Fine – use it for regulatory numbers. Just give me the real numbers as well.” If the answer is “We have modelled the market and the normal distribution is the best fit after considering the other possible distributions.” then your answer should be “Fine – thanks for that.”