Paper: arXiv 2605.00196

Authors: Tomasz J. Kozubowski, Andrey Sarantsev, James A. Spiker

Abstract

We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes significantly simpler than in the standard univariate case, reducing to a form of classical linear regression. We derive explicit expressions for the resulting estimators. For certain parameter configurations, the estimators exhibit nonstandard convergence rates, exceeding the usual square-root rate. Finally, we illustrate the applicability of this model in financial contexts by analyzing stock index returns and associated volatility for several major indices.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical derivation of a bivariate distribution and its maximum likelihood estimators, including nonstandard convergence rates and Fisher information analysis. While it mentions financial application, the empirical content is illustrative rather than a rigorous or comprehensive backtest, focusing primarily on the theoretical construction.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Model Stock Returns & Volatility using Bivariate Gamma Generalized Laplace Law] --> B[<b>Data Input:</b> Stock index returns + Observed gamma mixing variables]
    B --> C[<b>Methodology:</b> Formulate Bivariate Framework]
    C --> D[<b>Computation:</b> Simplify MLE to Linear Regression]
    D --> E[<b>Analysis:</b> Derive Estimators & Nonstandard Convergence Rates]
    E --> F[<b>Outcomes:</b> Efficient Parameter Estimation & Empirical validation on major indices]

Cited References (20)

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  8. The Laplace Distribution and Generalizations (2012) — link
and 12 more
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1 of 20 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.