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The $\kappa$-generalised Distribution for Stock Returns

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  • Samuel Forbes

Abstract

Empirical evidence shows stock returns are often heavy-tailed rather than normally distributed. The $\kappa$-generalised distribution, originated in the context of statistical physics by Kaniadakis, is characterised by the $\kappa$-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 $\kappa$-generalised distribution is a good fit for a significant proportion of the 200 stock returns analysed.

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  • Samuel Forbes, 2024. "The $\kappa$-generalised Distribution for Stock Returns," Papers 2405.09929, arXiv.org.
    • Handle: RePEc:arx:papers:2405.09929
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