Affine fractional stochastic volatility models

F. Comte, L. Coutin, E. Renault

Research output: Contribution to journalArticleResearchpeer-review

80 Citations (Scopus)


By fractional integration of a square root volatility process, we propose in this paper a long memory extension of the Heston (Rev Financ Stud 6:327-343, 1993) option pricing model. Long memory in the volatility process allows us to explain some option pricing puzzles as steep volatility smiles in long term options and co-movements between implied and realized volatility. Moreover, we take advantage of the analytical tractability of affine diffusion models to clearly disentangle long term components and short term variations in the term structure of volatility smiles. In addition, we provide a recursive algorithm of discretization of fractional integrals in order to be able to implement a method of moments based estimation procedure from the high frequency observation of realized volatilities.

Original languageEnglish
Pages (from-to)337-378
Number of pages42
JournalAnnals of Finance
Issue number2-3
Publication statusPublished - May 2012
Externally publishedYes


  • Fractional integrals
  • Integrated volatility
  • Long memory processes
  • Option pricing
  • Stochastic volatility

Cite this