path integral

The path integral method in interest rate models

An application of path integral method to Merton and Vasicek stochastic models of interest rate is considered.  Two approaches to a path integral construction are shown.  The first approach consists in using Wieners measure with the following substitution of solutions of stochastic equations into the models.  The second approach is realised by using transformation from Wieners measure to the integral measure related to the stochastic variables of Merton and Vasicek equations.  The introduction of boundary conditions is considered in the second approach in order to remove incorrect time asym