Using path integrals to price interest rate derivatives

Abstract

We present a new approach for the pricing of interest rate derivatives which allows a direct computation of option premiums without deriving a (Black-Scholes type) partial differential equation and without explicitly solving the stochastic process for the underlying variable. The approach is tested by rederiving the prices of a zero bond and a zero bond option for a short rate environment which is governed by Vasicek dynamics. Furthermore, a generalization of the method to general short rate models is outlined. In the case, where analytical solutions are not accessible, numerical implementations of the path integral method in terms of lattice calculations as well as path integral Monte Carlo simulations are possible.