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Affine representations of fractional processes with applications in mathematical finance

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  • Harms, Philipp
  • Stefanovits, David

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

  • Harms, Philipp & Stefanovits, David, 2019. "Affine representations of fractional processes with applications in mathematical finance," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1185-1228.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:4:p:1185-1228
    DOI: 10.1016/j.spa.2018.04.010
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    References listed on IDEAS

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