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Invariant measures for multidimensional fractional stochastic volatility models

Author

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  • Bal'azs Gerencs'er
  • Mikl'os R'asonyi

Abstract

We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to Markov chains in random environments in an efficient way.

Suggested Citation

  • Bal'azs Gerencs'er & Mikl'os R'asonyi, 2020. "Invariant measures for multidimensional fractional stochastic volatility models," Papers 2002.04832, arXiv.org, revised Aug 2021.
    • Handle: RePEc:arx:papers:2002.04832
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    References listed on IDEAS

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    1. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous‐time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323, October.
    2. Paolo Guasoni & Miklós Rásonyi, 2015. "Fragility of arbitrage and bubbles in local martingale diffusion models," Finance and Stochastics, Springer, vol. 19(2), pages 215-231, April.
    3. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2018. "Volatility is rough," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 933-949, June.
    4. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    5. Masaaki Fukasawa, 2017. "Short-time at-the-money skew and rough fractional volatility," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 189-198, February.
    6. Veretennikov, A. Yu., 1997. "On polynomial mixing bounds for stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 115-127, October.
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    Cited by:

    1. Rásonyi, Miklós & Tikosi, Kinga, 2022. "On the stability of the stochastic gradient Langevin algorithm with dependent data stream," Statistics & Probability Letters, Elsevier, vol. 182(C).

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