On term structure of yield rates. 3. The Duffie - Kan one-factor model | Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaja tehnika i informatika – Tomsk State University Journal of Control and Computer Science. 2012. № 3(20).

On term structure of yield rates. 3. The Duffie - Kan one-factor model

The time structure of interest rates plays a key role at the bond pricing. Therefore its propertiesinterest many financial analysts. However in the available literature usually there is a schematicdescription of these properties. Attempt of the detailed description of all possible forms oftime structure for a class of affine models of interest rates as for these models it is possible towrite down decisions in the closed form here becomes. As the basic the model of Duffie - Kan(DK) with any bottom border for risk free (spot) interest rate is accepted. Results for widelyknown models CIR and Vasiček turn out as special cases.For one-factor model of affine yield of Duffie - Kan analytical representations of yield curvesand forward curves are found and their properties when the duration measure of risk free rates asa time variable is used are investigated. It is shown that for all variety of parameters exists onlyfour possible kinds of yield curves. For small terms to maturity an bond yield is defined, basically,current level of risk free rates while for very long terms to maturity the yield is defined by astationary expectation of risk free rates. In this connection it would be possible to expect that influenceof current level of risk free rates on yield with time increase will damp. However it not so.It has appeared that current level of risk free rates essentially influences on sight of entire yieldcurve and a forward curve. Let's notice also that yield curve and a forward curve start from onepoint and at increase in term to maturity converge to the same limit that differs from usually acceptedpoint of view that these curves diverge when the term to maturity increase.

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Keywords

Duffie-Kan model, model CIR, Vasiček model, forward curve, yield curve, yield interest rates, affine model, модель Даффи - Кана, модель Кокса - Ингерсолла - Росса, модель Васичека, форвардная кривая, кривая доходности, аффинная модель, процентные ставки доходности

Authors

Name	Organization	E-mail
Medvedev Gennady A.	Belarusian State University	MedvedevGA@cosmostv.by

Всего: 1

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