A Hamiltonian Approach to Barrier Option Pricing Under Vasicek Model

In this paper, we study option pricing under Vasicek Model by a Hamiltonian approach. Since the interest rate changes with time, we split the time to maturity into infinite steps, and the matrix element during each step could be calculated by quantum mechanics methods. Using completeness condition, the pricing kernel and the integral expression of option price could also be derived. Numerical results of option prices as functions of underlying asset price, floating rate and regression rate are also shown.