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Wild Randomness, and the application of Hyperbolic Diffusion in Financial Modelling

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  • Will Hicks

Abstract

The application of the Cauchy distribution has often been discussed as a potential model of the financial markets. In particular the way in which single extreme, or "Black Swan", events can impact long term historical moments, is often cited. In this article we show how one can construct Martingale processes, which have marginal distributions that tend to the Cauchy distribution in the large volatility limit. This provides financial justification to approaches discussed by other authors, and highlights an example of how quantum probability can be used to construct non-Gaussian Martingales. We go on to illustrate links with hyperbolic diffusion, and discuss the insight this provides.

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  • Will Hicks, 2021. "Wild Randomness, and the application of Hyperbolic Diffusion in Financial Modelling," Papers 2101.04604, arXiv.org, revised Apr 2021.
    • Handle: RePEc:arx:papers:2101.04604
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    References listed on IDEAS

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    1. Will Hicks, 2019. "Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion," Papers 1911.11475, arXiv.org, revised Jan 2020.
    2. Jana, T.K. & Roy, P., 2012. "Pseudo Hermitian formulation of the quantum Black–Scholes Hamiltonian," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2636-2640.
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