On Term Structure of Yield Rates. 5. The Duffie – Kan Two Factor Model (Continuation)

Models of Daffie–Kan, describing dynamics of a short-term interest rate in a case when the state of the financial market is characterized not only by level of the interest rate, but also one more parameter changing in time are investigated. Two cases are considered. In the first in quality of an additional state variable the local on time average value of a short-term interest rate is taken. In the second case as an additional state variable the instant variance of an interest rate is accepted. Two-factor models are under construction so that they led to affine term structure of yield. The main attention is given to properties of yield curve and a forward curve when dynamics of a short-term interest rate is described by two-factor models of Daffie–Kan. Because functions of term structure for additional variables in a closed form can't be received, the type of curves as a whole (for entire interval of change of time) is analyzed by means of numerical calculations though properties of curves on the ends of an interval become clear analytically. For model «a rate – its local average» it is appeared that limiting properties of long-term yield are defined only by properties of an additional variable – local average of interest rates. For model «a rate – its instant variance» it became clear that this model has economic sense only when the weight factor of instant variance at determination of a short-term yield rate is equal to zero. Comparison of yield curves and forward curves for one-factor model and two-factor models shows that at the accepted parameters these curves considerably differ. As values of weight factors essentially influence behavior of yield curves and forward curves, they should be estimated along with market parameters of the price of risk