Determination of zero-coupon and spot rates from treasury data by maximum entropy methods

An interesting and important inverse problem in finance consists of the determination of spot rates or prices of the zero coupon bonds, when the only information available consists of the prices of a few coupon bonds. A variety of methods have been proposed to deal with this problem. Here we present variants of a non-parametric method to treat with such problems, which neither imposes an analytic form on the rates or bond prices, nor imposes a model for the (random) evolution of the yields. The procedure consists of transforming the problem of the determination of the prices of the zero coupon bonds into a linear inverse problem with convex constraints, and then applying the method of maximum entropy in the mean. This method is flexible enough to provide a possible solution to a mispricing problem.