A gamma time-changed fractional Brownian motion is a semimartingale, and the resulting five-parameter fractional Variance Gamma model fits S&P 500 return moments with H≈0.45.
Fractional iterated Ornstein-Uhlenbeck Processes
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abstract
In this work we present a Gaussian process that arise from the iteration of p fractional Ornstein-Uhlenbeck processes generated by the same fractional Brownian motion. This iteration results, when the values of lambdas are pairwise differents, in a particular linear combination of those processes. Although for $H>1/2$ each term of the linear combination is a long memory processes, we prove that it results in a short memory processes. We include applications to real data that show improvement in predictive performance compared with different ARMA models.
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Option Pricing with Time-Changed Fractional Brownian Motion: A Fractional Variance Gamma Model
A gamma time-changed fractional Brownian motion is a semimartingale, and the resulting five-parameter fractional Variance Gamma model fits S&P 500 return moments with H≈0.45.