Financial Simulation Modeling in Excel

DISTRIBUTIONS: NASSIM TALEB AND NORMALCY

One assumption that is commonly used in quantitative finance and in simulations is the normal, or Gaussian, distribution. Normal and lognormal distributions are related to the concept of Brownian motion (which we covered in Chapter 2). These concepts make assumptions about the relative likelihood of a price moving up or down, and the size of such a movement. Unfortunately, these assumptions are not exact representations of the how prices actually act much of the time. Extreme price movements have been observed to occur with a higher frequency than a normal distribution would lead us to predict.

After the mortgage meltdown of 2008, the use of normal distributions in finance was roundly criticized. One especially prominent voice in the denouncement of models using these distributions was Nassim Taleb, a highly regarded derivates trader and professor. Taleb is best known for his book The Black Swan: The Impact of the Highly Improbable, which was first published in 2007 and argued, among other things, that the statistical methods used in finance were dangerous because they led managers to think they knew more about potential outcomes than they actually did. This situation encourages certain actors to take (or allow) more risk than is prudent. Central to this argument is that extreme events are more likely than forecast in a normal distribution (a “fat-tail” or “heavy-tail” distribution may be more appropriate), and these extreme events have ...