Hedging options in market models modulated by the fractional Brownian motion

Boualem Djehiche, M'hamed Eddahbi

Research output: Contribution to journalArticlepeer-review


We use the stochastic calculus of variations for the fractional Brownian motion to derive formulas for the replicating portfolios for a class of contingent claims in a Bachelier and a Black-Scholes markets modulated by fractional Brownian motion. An example of such a model is the Black-Scholes process whose volatility solves a stochastic differential equation driven by a fractional Brownian motion that may depend on the underlying Brownian motion.

Original languageEnglish (US)
Pages (from-to)753-770
Number of pages18
JournalStochastic Analysis and Applications
Issue number5
StatePublished - 2001


  • Fractional Brownian motion
  • Hedging options
  • Stochastic calculus of variations
  • Stochastic volatility

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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