Fat Tail Option Calculator 1.0

The Fat Tail Option calculator makes use of Stable Distributions to estimate the theoretical value of European options. This provides a richer method with a better fit to real data and real capital market behavior than the common Black-Scholes formula. Especially, it can be used to take into account the existence of crash events.

The Fat Tail Option Calculator is available as a stand-alone application or as an Add-in to MS Excel. It is available as a free download.

See also the Fractal Financial Markets essay.

System Requirements
The Fat Tail Option Calculator requires Windows NT 4.0 or later or Windows 95 or later. If you want to use the Excel Add-in, Excel 97 or later is required.

As there are millions of complex numerical calculations involved in calculating the value of an option using stable distributions, we recommend that you use a modern computer with at least a Pentium 400 MHz processor.

Mathematical background
The most common way to estimate the value of options is to use the Black-Scholes formula. If the price changes of a security are log-normally distributed, the Black-Scholes formula provides the theoretical price of so called European options on that security. Unfortunately, there is overwhelming evidence that price changes are not log-normally distributed. Instead, security price changes have what is often called fat tails. They also exhibit skewness. Fat tails can be modeled with so called Stable Distributions, also called Levy distributions and Levy-Pareto distributions. A Normal or Gaussian distribution is a special case of a stable distribution. The Cauchy distribution is another well known example of a stable distribution. In fact, the Gaussian and the Cauchy distributions are the only two stable distributions for which closed form mathematical formulas exist.