Path Integral Method for Pricing Proportional Step Double-Barrier Option with Time Dependent Parameters

TL;DR

This paper introduces a path integral approach to price proportional step double-barrier options with time-dependent parameters, drawing analogies from quantum mechanics to derive a new pricing kernel.

Contribution

The paper develops a novel path integral method for pricing PDBS options with time-dependent interest rates and volatility, extending quantum mechanics techniques to finance.

Findings

Derived the pricing kernel for PDBS options with time-dependent parameters

Numerical results demonstrate the method's effectiveness

Path integral approach can be generalized to curved boundary options

Abstract

Path integral method in quantum mechanics provides a new thinking for barrier option pricing. For proportional double-barrier step (PDBS) options, the option price changing process is analogous to a particle moving in a finite symmetric square potential well. We have derived the pricing kernel of PDBS options with time dependent interest rate and volatility. Numerical results of option price as a function of underlying asset price are shown as well. Path integral method can be easily generalized to the pricing of PDBS options with curved boundaries.