Saturday, November 24, 2007
Detecting Non Gaussianity in Option Pricing
One of the problems of calculating the worth of options by the Black Scholes method, is that it works only for Gaussian data. When the distribution is different ("fat tail" or to coin a word, Talebian) the equation makes problems. There are some statistical tests and methods to detect non-Gaussianity, non-stationarity, and non-linearity in the data that could be applied to stock exchange happenings. A classical test for a sequence of data to be Gaussian is the Kolmogorov–Smirnov test. It calculates the maximum distance between the cumulative distribution of the data and that of a normal distribution, and assesses the significance of the distance. A similar test is the Lillifors test, but it adjusts for the fact that the parameters of the normal distribution are estimated from the data rather than specified in advance. Another test is the Jarque–Bera test which determines whether sample skewness and kurtosis are unusually different from their Gaussian values. One of the reasons I lost money in my options (and most in oil shorting) is the use of bad math representations. I have no time to work on this problem, hope somebody will do it for me and publish it.