On Term Structure of Yield Rates. 1. Vasiček Model

The time structure, interesting to experts and researchers, is the nominal yield curve that represents the yields to maturity for nominal bonds (i.e. the bonds that are issued at a face-value and have the coupons with the same yields). Determination of nominal yield curve is based on observation of the state securities being in circulation just sold at auction and most liquid. These securities in the countries with the developed economy are issued for 10 initial terms to maturity. They are issued usually at a face-value and to their yield rates are called as yield of nominal bonds. Determination of time structure of interest rates is reduced to that having only 10 nominal yields being in circulation directly observed in the market, and using other information contained in the description of these securities it is necessary to design the function, allowing to calculate yields for any term to maturity. In the paper properties of such characteristics of time structure of interest rates as yield curve and forward rates in a case when the affine model of yield is used are researched. Unlike known approaches are analyzed not only one-factor, but also multifactor models. Besides, it is considered not only a range of short and middle terms to maturity of securities, but also long terms. For multifactor models of affine yields the analytical representations of yield curves and forward curves are found. In addition instead of time variable it is offered to use the risk-free rate durations. It gives the enable for comparisons of yield curves and forward curves for every possible entire interval of change of term to maturities of assets.