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

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.