A Fractional Version of the Heston Model with Hurst Parameter H ∈ (1/2, 1)
12 Pages Posted: 13 Dec 2016
Date Written: December 12, 2016
We consider a fractional version of the Heston model where the two standard Brownian motions are replaced by two fractional Brownian motions with Hurst parameter H ∈ (1/2, 1). We show that the stochastic differential equation admits a unique positive solution by adapting and generalizing some results of Y. Hu, D. Nualart and X. Song on singular equations driven by rough paths. Moreover, we show that the fractional version of the variance, which is a version of the fractional Cox-Ingersoll-Ross model, is still a mean-reverting process.
Keywords: fractional Heston and Cox-Ingersoll-Ross models, fractional Brownian motion, singular equations driven by rough paths
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