On Yield Curves of the European Central Bank

In this paper it is showed that the yield curve of the European Central Bank (ECB) does not satisfy the no arbitrage conditions. To construct a no-arbitrage yield curve, we need to add one more term to yield curve. As the state variables, it is necessary to choose a four-dimensional diffusion Gaussian process. Fifth factor is determined from the no arbitrage conditions. The version of the modification of the yield curve proposed in the paper differs from the earlier proposed modifications in order to ensure the absence of arbitrage opportunities. Application of no arbitrage conditions to the Duffie-Kan model (with a square-root volatility), into which the Vasiček and Cox-Ingersoll-Ross models are being embedded, gives preference to the four-factor Vasiček model