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The t -Distribution in Financial Mathematics and Multivariate Testing Contexts

Author

Listed:
  • Eugene Seneta

    (School of Mathematics and Statistics, F07, The University of Sydney, Darlington, NSW 2006, Australia
    These authors contributed equally to this work.)

  • Thomas Fung

    (School of Mathematical and Physical Sciences, Macquarie University, North Ryde, NSW 2109, Australia
    These authors contributed equally to this work.)

Abstract

The Student’s t -distribution provides a thematic connection between the historical and technical elements of this paper. The historical section offers a brief account of the early contributions of Chris Heyde and his collaborations with Madan and Seneta in the development of financial mathematics. The technical section focuses on hypothesis testing, motivated by the observation that, in a setting with pairwise exchangeable dependence for test statistics, the cutoff methods proposed by Sarkar and colleagues in 2016 can be viewed as a first iteration of the classical approach developed by Holm in 1979. These methods had already been refined earlier by Seneta and Chen in their work from 1997 and 2005, which laid the foundation for further improvements. Building on this, a new iteration of the Seneta-Chen method is presented, offering enhancements over the Sarkar approach. Numerical and graphical comparisons are provided, focusing on equal tails testing within the multivariate t -distribution framework. While the tabulated results clearly show improvements with the new procedure, the simulated family-wise error rates across varying correlations reveal only minor practical differences between the iterative methods. This suggests that, under suitable conditions, a single iteration suffices in practice. The paper concludes with personal reflections from the first author, sharing memories of Joe Gani and Chris Heyde, in keeping with the commemorative nature of this issue.

Suggested Citation

  • Eugene Seneta & Thomas Fung, 2025. "The t -Distribution in Financial Mathematics and Multivariate Testing Contexts," JRFM, MDPI, vol. 18(5), pages 1-20, April.
    • Handle: RePEc:gam:jjrfmx:v:18:y:2025:i:5:p:224-:d:1639976
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    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Sanat K. Sarkar & Yiyong Fu & Wenge Guo, 2016. "Improving Holm's procedure using pairwise dependencies," Biometrika, Biometrika Trust, vol. 103(1), pages 237-243.
    3. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
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