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Fractional processes have gained popularity in financial modeling due to thedependence structure of their increments and the roughness of their samplepaths. The non-Markovianity of these processes gives, however, rise toconceptual and practical difficulties in computation and calibration. Toaddress these issues, we show that a certain class of fractional processes canbe 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 examplesthat this allows one to construct tractable financial models with fractionalfeatures.

Affine representations of fractional processes with applications in mathematical finance