(National University of Lesotho, 2022-10-21) Ramoeletsi, Realeboha; Kaibe, Bosiu, Ngaka Nchejane
We perform Lie symmetry analysis to the fractional Black-Scholes option pricing model
whose price evolution is described in terms of a partial di erential equation (PDE). As a
result, new complete Lie symmetry group and in nitesimal generators of the one-dimensional
fractional Black-Scholes pricing model are derived. Furthermore, we compute a family of
exact invariant solutions that constitute the pricing models for the Black-Scholes model using
the associated in nitesimal generators and the corresponding similarity reduction equations.
Using known solutions, more solutions are generated via group point transformations