Abstract
The processes of short-term interest rates generate changes in most market indices, as well as form the basis of determining the value of marketable assets and commercial contracts. They play a special role in calculating the term structure of the yield. Therefore, the development of mathematical models of these processes is extremely interesting for financial analysts and researchers of market issues. There are many versions of change of short-term risk-free interest rates in the framework of the theory of diffusion processes. However, there is still no such model, which would be the basis for building a term structure of yields close to that existing in a real financial market. It is interesting to analyze the existing models in order to clarify features of models in a probabilistic sense in more detail than has been done by their creators and users. Such an analysis will be made here for the family of models used by the authors in three well-known papers [1–3], where they were applied for the fitting of the real time series of yield.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
CKLS: Chan, K.C., Karolyi, G.A., Longstaff, F.A., Sanders, A.S.: An empirical comparison of alternative models of the short-term interest rate. J. Finance 47, 1209–1227 (1992)
Ahn, D.-H., Gao, B.: A parametric nonlinear model of term structure dynamics. Rev. Finan. Stud. 12(4), 721–762 (1999)
Bali, T.: An empirical comparison of continuous time models of the short term interest rate. J. Futures Markets 19(7), 777–797 (1999)
Vasicek, O.A.: An equilibrium characterization of the term structure. J. Finan. Econ. 5, 177–188 (1977)
CIR: Cox, J.C., Ingersoll, J.E., Ross, S.A.: A theory of the term structure of interest rate. Econometrica 53, 385–467 (1985)
Duffie, D., Kan, R.: A yield-factor model of interest rates. Math. Finance. 6, 379–406 (1996)
Black, F., Derman, E., Toy, W.: A one factor model of interest rates and its application to treasury bond options. Finan. Anal. J. 46(1), 33–39 (1990)
Ait-Sahalia, Y.: Testing continuous-time models of the spot interest rate. Rev. Finan. Stud. 9(2), 385–426 (1996)
Brennan, M.J., Schwartz, E.S.: A continuous time approach to the pricing of bond. J. Bank. Finance 3, 135–155 (1979)
CIR: Cox, J.C., Ingersoll, J.E., Ross, S.A.: An analysis of variable rate loan contracts. J. Finance 35, 389–403 (1980)
Cox, J.C., Ross, S.A.: The valuation of options for alternative stochastic processes. J. Finan. Econ. 3, 145–166 (1976)
Merton, R.C.: Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4(1), 141–183 (1973)
Dothan, M.: On the term structure of interest rates. J. Finan. Econ. 6, 59–69 (1978)
Samuelson, P.A.: Rational theory of warrant pricing. Ind. Manag. Rev. 6, 13–31 (1965)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Medvedev, G. (2016). Probability Properties of Interest Rate Models. In: Dudin, A., Gortsev, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2016. Communications in Computer and Information Science, vol 638. Springer, Cham. https://doi.org/10.1007/978-3-319-44615-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-44615-8_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-44614-1
Online ISBN: 978-3-319-44615-8
eBook Packages: Computer ScienceComputer Science (R0)