Barrier Option Pricing

TL;DR

This paper applies Lie symmetry methods to price barrier options, overcoming previous limitations related to the smoothness of the payoff function, and deriving new solutions for these financial derivatives.

Contribution

It introduces a novel application of Lie symmetry analysis to barrier option pricing, enabling solutions where traditional methods face restrictions.

Findings

Derived new analytical solutions for barrier options

Extended Lie symmetry methods to handle non-smooth payoff functions

Provided a framework for future analytical pricing models

Abstract

We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not smooth. However, for barrier options, this restriction can be accommodated and a symmetry analysis utilised to find new solutions.