The no arbitrage conditions are derived in the explicit form for the market, where the zero coupons bonds of various maturities are accessible for the investors to draw up the portfolios. It is supposed, that the investor at any moment of time has a possibility to make the self-financed...

This paper examines the market price of risk for discount bond prices under an affine term structure of interest rates. The usual relation plays two roles. First, it is the definition of market price of risk and, second, it provides a no arbitrage condition for the discount bond market. Here the...

This paper considers a problem of asset pricing for case when the short-term interest rate process does not have the markovian property. In this case the price can be determined also by state variables some of that are not observable. In the same time from the practical point of view, the...

Processes of the interest rates and other financial indexes in continuous time are usually modeled in the literature by stochastic processes with independent increments. Such processes are described by the stochastic differential equations and are the Markov processes. As it follows from the...

The multi-factor model “with square root” is discussed in details. For such model, the representation of state variable process in the integral form is derived and its covariance matrix is found. The special attention to the problem connected with the tendency for the term structure of...

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 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...