A Hamiltonian Approach to Floating Barrier Option Pricing

TL;DR

This paper introduces a Hamiltonian-based method for pricing floating barrier options, drawing analogies from quantum mechanics to derive analytical formulas and validate them with numerical results.

Contribution

It applies Hamiltonian techniques from quantum mechanics to derive analytical pricing formulas for floating barrier options, a novel approach in financial mathematics.

Findings

Analytical expressions for pricing kernels and option prices were derived.

Numerical results align with traditional mathematical calculations.

The method provides a new perspective for barrier option pricing.

Abstract

Hamiltonian approach in quantum mechanics provides a new thinking for barrier option pricing. For proportional floating barrier step options, the option price changing process is similar to the one dimensional trapezoid potential barrier scattering problem in quantum mechanics; for floating double-barrier step options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well. Using Hamiltonian methodology, the analytical expressions of pricing kernel and option price could be derived. Numerical results of option price as a function of underlying price, floating rate, interest rate and exercise price are shown, which are consistent with the results given by mathematical calculations.