Price Modelling under Generalized Fractional Brownian Motion

Varování

Publikace nespadá pod Pedagogickou fakultu, ale pod Ekonomicko-správní fakultu. Oficiální stránka publikace je na webu muni.cz.

Autoři	ARANEDA Axel Alejandro
Rok publikování	2024
Druh	Kapitola v knize
Fakulta / Pracoviště MU	Ekonomicko-správní fakulta
Citace
Popis	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 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.