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On Time-subordinated Brownian Motion Processes for Financial Markets

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  • Rohan Shenoy
  • Peter Kempthorne

Abstract

In the context of time-subordinated Brownian motion models, Fourier theory and methodology are proposed to modelling the stochastic distribution of time increments. Gaussian Variance-Mean mixtures and time-subordinated models are reviewed with a key example being the Variance-Gamma process. A non-parametric characteristic function decomposition of subordinated Brownian motion is presented. The theory requires an extension of the real domain of certain characteristic functions to the complex plane, the validity of which is proven here. This allows one to characterise and study the stochastic time-change directly from the full process. An empirical decomposition of S\&P log-returns is provided to illustrate the methodology.

Suggested Citation

  • Rohan Shenoy & Peter Kempthorne, 2025. "On Time-subordinated Brownian Motion Processes for Financial Markets," Papers 2510.14108, arXiv.org, revised Oct 2025.
    • Handle: RePEc:arx:papers:2510.14108
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    References listed on IDEAS

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    5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
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