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Strong convergence rates for Markovian representations of fractional processes

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  • Philipp Harms

Abstract

Many fractional processes can be represented as an integral over a family of Ornstein-Uhlenbeck processes. This representation naturally lends itself to numerical discretizations, which are shown in this paper to have strong convergence rates of arbitrarily high polynomial order. This explains the potential, but also some limitations of such representations as the basis of Monte Carlo schemes for fractional volatility models such as the rough Bergomi model.

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  • Philipp Harms, 2019. "Strong convergence rates for Markovian representations of fractional processes," Papers 1902.01471, arXiv.org, revised Aug 2020.
    • Handle: RePEc:arx:papers:1902.01471
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    References listed on IDEAS

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    1. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    2. Paul Gassiat, 2018. "On the martingale property in the rough Bergomi model," Papers 1811.10935, arXiv.org, revised Apr 2019.
    3. Maximilian Ga{ss} & Kathrin Glau & Mirco Mahlstedt & Maximilian Mair, 2015. "Chebyshev Interpolation for Parametric Option Pricing," Papers 1505.04648, arXiv.org, revised Jul 2016.
    4. Maximilian Ga{ss} & Kathrin Glau & Maximilian Mair, 2015. "Magic points in finance: Empirical integration for parametric option pricing," Papers 1511.00884, arXiv.org, revised Nov 2016.
    5. Masaaki Fukasawa, 2011. "Asymptotic analysis for stochastic volatility: martingale expansion," Finance and Stochastics, Springer, vol. 15(4), pages 635-654, December.
    6. Blanka Horvath & Antoine Jacquier & Aitor Muguruza & Andreas Sojmark, 2017. "Functional central limit theorems for rough volatility," Papers 1711.03078, arXiv.org, revised Nov 2023.
    7. Philippe Carmona & Laure Coutin & G. Montseny, 2000. "Approximation of Some Gaussian Processes," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 161-171, January.
    8. Christian Bayer & Peter K. Friz & Paul Gassiat & Joerg Martin & Benjamin Stemper, 2017. "A regularity structure for rough volatility," Papers 1710.07481, arXiv.org.
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    Cited by:

    1. Ozan Akdogan, 2019. "Vol-of-vol expansion for (rough) stochastic volatility models," Papers 1910.03245, arXiv.org, revised Dec 2019.
    2. Peter Carr & Andrey Itkin, 2019. "ADOL - Markovian approximation of rough lognormal model," Papers 1904.09240, arXiv.org.

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