Application of lie symmetrics to solving fractional black-scholes option pricing model in financial mathematics
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Date
2022-10-21
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National University of Lesotho
Abstract
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
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Keywords
Lie point symmetries, fractional Black-Scholes, option pricing, financial mathematics