Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricing

TL;DR

This paper applies the path integral method from quantum mechanics to derive analytical pricing formulas for proportional step and double-barrier step options, providing a novel approach to barrier option valuation.

Contribution

It introduces a new application of the path integral method to barrier option pricing, deriving analytical expressions for the pricing kernel and option prices.

Findings

Analytical pricing formulas are derived for the options.

Numerical results align with traditional mathematical methods.

The method offers a new perspective on barrier option valuation.

Abstract

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