  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.
