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Affine representations of fractional processes with applications in mathematical finance

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  • Philipp Harms
  • David Stefanovits

Abstract

Fractional processes have gained popularity in financial modeling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we show that a certain class of fractional processes can be represented as linear functionals of an infinite dimensional affine process. This can be derived from integral representations similar to those of Carmona, Coutin, Montseny, and Muravlev. We demonstrate by means of several examples that this allows one to construct tractable financial models with fractional features.

Suggested Citation

  • Philipp Harms & David Stefanovits, 2015. "Affine representations of fractional processes with applications in mathematical finance," Papers 1510.04061, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1510.04061
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    References listed on IDEAS

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    1. Rui Vilela Mendes & M. J. Oliveira, 2006. "A data-reconstructed fractional volatility model," Papers math/0602013, arXiv.org, revised Jun 2007.
    2. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    3. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    4. 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.
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    1. repec:hal:wpaper:hal-02265210 is not listed on IDEAS
    2. Nicole Bauerle & Sascha Desmettre, 2018. "Portfolio Optimization in Fractional and Rough Heston Models," Papers 1809.10716, arXiv.org, revised May 2019.
    3. Abi Jaber, Eduardo & El Euch, Omar, 2019. "Markovian structure of the Volterra Heston model," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 63-72.
    4. Martin Keller-Ressel & Martin Larsson & Sergio Pulido, 2018. "Affine Rough Models," Papers 1812.08486, arXiv.org.

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