Fitting Zero-coupon Yield Curve in the Russian Bond Market
In this paper we present a new nonparametric approach for fitting the zero-coupon yield curve to coupon bond quotes. Unlike other existing methods, our method has a number of advantages: the ability to fit complex zero-coupon yield curve shapes, the absence of the need to manually choose the smoothing parameter, the ability to ensure the positiveness of the fitted instantaneous forward rates, incorporating market liquidity information, and consistency with a no-arbitrage stochastic model. Usually nonparametric methods require apriori knowledge about the ratio of accuracy of the solution and smoothness of the term structure. The novelty of proposed method is in the automatic determination of this parameter by using cross-validation method. We discuss various modifications of the method to incorporate individual preferences of a decision maker used yield curve. For example, one can reflect the horizontal yield in yield curve after certain time to maturity or set own relative/absolute scale for non-smoothness of yield curve. Alternative methods often assume that bond prices are accurately known. We depart from this assumption by taking into account a possible error of input data (bond prices). We assume that the order of the error is reflected in the bid-ask spread. This allows on the one hand to take into account possible errors and/or inaccuracy of the original data, and on the other hand to build a zero-coupon yield curves are smooth. On Russian bond market data we compare the proposed method with several alternatives for a number of widespread popular quality criteria used for comparison of this kind of methods that reflect the accuracy of the result, and the smoothness of the resulting curves. The results of the comparison indicate the superiority of the proposed method for all criteria.