| The basic problem in estimating the interest rate term structure, what means that prices of coupon bonds have to be used. It is, however, well-known that the actuarial return of the bond is not a good measure.; We present a method determining directly the forward rate curve, based on the optimization of a measure of degree of smoothness subject to some no arbitrage restrictions. Furthermore, the existence of some disturbances in the no arbitrage relations is allowed.; The advantage of this method over the already existing spline methods is that the number and the location of the knots are determined by the observed data itself. Furthermore, smooth forward rate curves that do not fluctuate much and tend to flatten towards the end, are obtained.; The method is presented in a continuous as well as in a discrete time framework. Necessary and sufficient conditions to obtain the continuous optimal curve are derived and some practical solving methods are discussed. Furthermore, it is proved that the discrete solution coverages uniformly to the continuous one when the discretization step goes to zero. Finally, examples are presented based on real or simulated data. |
