The sub-fractional Brownian motion (sfBm) could be considered as the intermediate step between the standard Brownian motion (Bm) and the fractional Brownian motion (fBm). By the way, subfractional diffusion is a candidate to describe stochastic processes with long-range dependence and non-stationarity in their increments. In this note, we use sfBm for financial modeling. In particular, we extend the results provided by Araneda [Axel A. Araneda. The fractional and mixed-fractional CEV model. Journal of Computational and Applied Mathematics, 363:106-123, 2020] arriving at the option pricing under the sub-fractional CEV model.
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