A CONSTRAINED LEAST SQUARE METHOD FOR ESTIMATING A SMOOTH, NONNEGATIVE FORWARD RATE SEQUENCE

摘要

We will develop an efficient method for estimating a smooth nonnegative forward rate sequence using the market price of riskless bonds. This method is an improvement of the classical Carleton-Cooper's method based on standard least square method, which often generates a non-smooth forward rate sequence and hence is not used in practice. The method to be proposed in this paper is intended to resolve this difficulty. We will impose a smoothness condition while maintaining the fitting error within an acceptable level. The resulting optimization problem is shown to be convex in the region of interest. Therefore, we can calculate a globally optimal solution very fast by standard nonlinear programming algorithms. We will demonstrate that this method generates a smooth forward rate sequence at the expense of a very small increase of fitting error.