A Hamiltonian Approach to Barrier Option Pricing Under Vasicek Model

Hamiltonian approach in quantum theory provides a new thinking for option pricing with stochastic interest rates. For barrier options, the option price changing process is similar to the infinite high barrier scattering problem in quantum mechanics; for double barrier options, the option price changing process is analogous to a particle moving in a infinite square potential well. Using Hamiltonian approach, the expressions of pricing kernels and option prices under Vasicek stochastic interest rate model could be derived. Numerical results of options price as functions of underlying prices are also shown.
Comment: 18 pages,5 figures