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The roughness exponent and its model-free estimation

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  • Xiyue Han
  • Alexander Schied

Abstract

Motivated by pathwise stochastic calculus, we say that a continuous real-valued function $x$ admits the roughness exponent $R$ if the $p^{\text{th}}$ variation of $x$ converges to zero if $p>1/R$ and to infinity if $p

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  • Xiyue Han & Alexander Schied, 2021. "The roughness exponent and its model-free estimation," Papers 2111.10301, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2111.10301
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    References listed on IDEAS

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    1. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
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    3. Alexander Schied & Iryna Voloshchenko, 2015. "Pathwise no-arbitrage in a class of Delta hedging strategies," Papers 1511.00026, arXiv.org, revised Jun 2016.
    4. Han, Xiyue & Schied, Alexander & Zhang, Zhenyuan, 2021. "A probabilistic approach to the Φ-variation of classical fractal functions with critical roughness," Statistics & Probability Letters, Elsevier, vol. 168(C).
    5. Hans Follmer & Alexander Schied, 2013. "Probabilistic aspects of finance," Papers 1309.7759, arXiv.org.
    6. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
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