The equation of term structure for the price of a zero-coupon bond is considered, the solution of which in analytical form is known, basically, for the simplest models and has an affine structure with respect to the short-term rate. In this paper, we construct solutions of this equation for a...

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...

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...

The paper presents a mathematically equivalent, but more compact description of the usually occurring quadratic model of yield. Equations for the functions of the term structure are obtained and general properties of their solutions are given. The main content of the paper is to consider the...

The Longstaff – Schwartz model is considered both in the space of latent state variables and in the space of observable (or estimated) state variables. Analytical expressions for yield curves to maturity and forward curves are obtained in both cases. Based on the analysis of the Longstaff –...

The possibility of representation of yield term structures in the form of polynomials or power series in models where short-term interest rate processes are described by stochastic differential equations is considered. In most diffusion models of short-term interest rate processes the functions...

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...

Interest rate models in which the short-term rate is a unique state variable are usually considered. These models are attractive that analytical decisions often give the chance to receive and provide concerning the simple computing analysis. However one-factor models have certain lacks. Basic of...

The paper studies the properties of curves of yield to maturity and forward rates curves for multifactorial and three concrete two-factor Vasiček models with two state variables:• The short-term rate and its average local-in-time value; • The short-term rate and its exponentially smoothed...

Within framework of the theory of diffusion processes there are various versions of an evolution of short-term yield interest rates. Nevertheless till now there was no such model which could be a suitable basis for construction of term structure of yield close to existing on real financial...