Affine representations of fractional processes with applications in mathematical finance

Philipp Harms and David Stefanovits

Stochastic Processes and their Applications, 2019, vol. 129, issue 4, 1185-1228

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.

Keywords: Fractional process; Markovian representation; Affine process; Infinite-dimensional Markov process; Fractional interest rate model; Fractional volatility model (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (26)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:4:p:1185-1228

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DOI: 10.1016/j.spa.2018.04.010

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