On the Nelson-Siegel-Svensson No-Arbitrage Yield Curve Models

It is shown that the requirement to satisfy the no-arbitrage conditions specifies the Nelson–Siegel–Svensson model in the sense that gives for coefficients of this model the obvious economic sense: the free coefficient should be function on term to maturity, and other coefficients should depend on the market state variables which, in turn, are selective values of stochastic processes at time point for which the time structure is designed. We will notice that the description of stochastic processes is produced under objective probability measure, i.e. taking into account risk market prices. It is shown that the model is the member of family of affine yield models and is generated by two-dimensional model of a short-term interest rate for Nelson–Siegel (NS) model or four-dimensional model of a short-term interest rate for Nelson–Siegel–Svensson (NSS) model. Stochastic processes, underlying NS- and NSS-models, are generated by the linear stochastic differential equations. In this connection the market state variables have normal distribution and can take with positive probability negative values. That is a certain lack of models NS and NSS