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Path integral method in quantum mechanics provides a new thinking for barrieroption pricing. For proportional step options, the option price changingprocess is similar to the one dimensional trapezoid potential barrierscattering problem in quantum mechanics; for double-barrier step options, theoption price changing process is analogous to a particle moving in a finitesymmetric square potential well. Using path integral method, the analyticalexpressions of pricing kernel and option price could be derived. Numericalresults of option price as a function of underlying price, potential andexercise price are shown, which are consistent with the results given bymathematical method.

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