Price modelling under generalized fractional Brownian motion

Axel A. Araneda

Papers from arXiv.org

Abstract: The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its use as the main driver for price fluctuations, replacing the standard Brownian Brownian motion in the well-known Black-Scholes model. By the derivation of the generalized fractional Ito's lemma and the related effective Fokker-Planck equation, we discuss its application to both the option pricing problem valuing European options, and the computation of Value-at-Risk and Expected Shortfall. Moreover, the option prices are computed for a CEV-type model driven by gfBm.

Date: 2021-08, Revised 2023-11
New Economics Papers: this item is included in nep-isf
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