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Hamiltonian approach in quantum theory provides a new thinking for optionpricing with stochastic interest rates. For barrier options, the option pricechanging process is similar to the infinite high barrier scattering problem inquantum mechanics; for double barrier options, the option price changingprocess is analogous to a particle moving in a infinite square potential well.Using Hamiltonian approach, the expressions of pricing kernels and optionprices under Vasicek stochastic interest rate model could be derived. Numericalresults of options price as functions of underlying prices are also shown.

A Hamiltonian Approach to Barrier Option Pricing Under Vasicek Model