Path Integral Method for Barrier Option Pricing Under Vasicek Model

Abstract

Path integral method in quantum theory provides a new thinking for time dependent option pricing. 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 path integral method, the expressions of pricing kernel and option price under Vasicek stochastic interest rate model could be derived. Numerical results of options price as functions of underlying prices are also shown.