The $κ$-generalised Distribution for Stock Returns

ArXiv ID: 2405.09929 “View on arXiv”

Authors: Unknown

Abstract

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.

Keywords: κ-generalised distribution, heavy-tailed distribution, FTSE 100, Nasdaq, Monte-Carlo simulation, Equity

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper introduces advanced statistical physics concepts (κ-exponential, entropy maximization) and complex MLE fitting for non-standard distributions, requiring significant mathematical density. Empirically, it includes real-world daily data for 200 stocks, uses Monte Carlo goodness-of-fit tests with Kolmogorov-Smirnov statistics, and reports p-values, demonstrating strong data-driven validation.

  flowchart TD
    A["Research Goal<br>Find suitable distribution<br>for heavy-tailed stock returns"] --> B{"Methodology"}
    B --> C["Data Source<br>Historic Daily Returns<br>FTSE 100 & Nasdaq Top 100"]
    B --> D["Model<br>Kappa-generalised distribution<br>Physics origin via Kaniadakis"]
    C --> E["Computational Process<br>Fit distribution to 200 stocks"]
    D --> E
    E --> F["Validation<br>Monte-Carlo Goodness-of-Fit Test"]
    F --> G["Key Outcome<br>Significant proportion of stocks<br>fitted successfully<br>Validating K-dist for finance"]