The κ-generalised Distribution for Stock Returns

Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The κ-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the κ-exponential function that is asymptotically exponential for small values and asymptotically power law for large values. This proves to be a useful property and makes it a good candidate distribution for many types of quantities. In this paper we focus on fitting historic daily stock returns for the FTSE 100 and the top 100 Nasdaq stocks. Using a Monte-Carlo goodness of fit test there is evidence that the κ-generalised distribution is a good fit for a significant proportion of the 200 stock returns analysed.