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Creating Tail Dependence by Rough Stochastic Correlation Satisfying a Fractional SDE; An Application in Finance

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  • László Márkus

    (Department of Probability Theory and Statistics, Eötvös Loránd University, 1117 Budapest, Hungary)

  • Ashish Kumar

    (Department of Probability Theory and Statistics, Eötvös Loránd University, 1117 Budapest, Hungary)

  • Amina Darougi

    (Doctoral School of Mathematics, Eötvös Loránd University, 1117 Budapest, Hungary)

Abstract

The stochastic correlation for Brownian motions is the integrand in the formula of their quadratic covariation. The estimation of this stochastic process becomes available from the temporally localized correlation of latent price driving Brownian motions in stochastic volatility models for asset prices. By analyzing this process for Apple and Microsoft stock prices traded minute-wise, we give statistical evidence for the roughness of its paths. Moment scaling indicates fractal behavior, and both fractal dimensions (approx. 1.95) and Hurst exponent estimates (around 0.05) point to rough paths. We model this rough stochastic correlation by a suitably transformed fractional Ornstein–Uhlenbeck process and simulate artificial stock prices, which allows computing tail dependence and the Herding Behavior Index (HIX) as functions in time. The computed HIX is hardly variable in time (e.g., standard deviation of 0.003–0.006); on the contrary, tail dependence fluctuates more heavily (e.g., standard deviation approx. 0.04). This results in a higher correlation risk, i.e., more frequent sudden coincident appearance of extreme prices than a steady HIX value indicates.

Suggested Citation

  • László Márkus & Ashish Kumar & Amina Darougi, 2025. "Creating Tail Dependence by Rough Stochastic Correlation Satisfying a Fractional SDE; An Application in Finance," Mathematics, MDPI, vol. 13(13), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:13:p:2072-:d:1685378
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    References listed on IDEAS

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