Abstract
We show that the sum of a Brownian motion and a non-trivial multiple of an independent fractional Brownian motion with Hurst parameter H ∈ (0,1] is not a semimartingale if H ∈ (0, ½) ∪ (½, ¾], that it is equivalent to a multiple of Brownian motion if H = ½ and equivalent to Brownian motion if H ∈ ( ¾ , 1]. As an application we discuss the price of a European call option on an asset driven by a linear combination of a Brownian motion and an independent fractional Brownian motion.
Citation
Patrick Cheridito. "Mixed fractional Brownian motion." Bernoulli 7 (6) 913 - 934, December 2001.
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