Barycentric Approximation of Stochastic Interest Rate Processes

The incorporation of single-factor interest rate models within the stochastic programming methodology is investigated and applied to multiperiod investment. Barycentric approximation is used for discretizing the stochastic factors and for generating scenario trees which take the various term structure movements into account. It is shown that employing the Vasicek model for the instantaneous rate process preserves convexity of the stochastic multistage program and, hence, guarantees information on the accuracy of the approximate investment strategies. To the contrary, the convexity of the program cannot be assessed if the square root process due to Cox-Ingersoll-Ross is used for the instantaneous rate. In this case, the approximate investment policies and their associated interest surplus may be accepted as estimates. Numerical results for 8-period and 6-period investment problems are discussed.