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2008 | 114 | 3 | 613-618
Article title

Modelling of Short Term Interest Rate Based on Fractional Relaxation Equation

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EN
Abstracts
EN
In this paper, we try to model the dynamics of short term interest rate using the fractional nonhomogeneous differential equation with stochastic free term. This type of equation is similar to one which represents the viscoelastic behavior of certain materials from rheologic point of view. As a final result we obtain the closed formula for prices of zero-coupon bonds. They are analogous to those in Vasiček model, where instead of the exponential functions we have the Mittag-Leffler ones.
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EN
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Year
Volume
114
Issue
3
Pages
613-618
Physical description
Dates
published
2008-09
received
2007-11-22
Contributors
author
  • Institute of Mathematics and Cryptology, Military University of Technology, Kaliskiego 2, 00-908 Warszawa, Poland
References
  • 1. R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics. Correlations and Complexity in Finance, Cambridge University Press, Cambridge 2000, p. 158
  • 2. M. Kozłowska, R. Kutner, Acta Phys. Pol. B 37, 3027 (2006)
  • 3. M. Kozłowska, A. Kasprzak, R. Kutner, Int. J. Mod. Phys. C 191, 08
  • 4 (20P. Billingsley, . Probability and Measure), Wiley, New York 1979, p. 600
  • 5. D. Heath, in: Introduction to Mathematical Finance, Eds. D. Heath, G. Swindle, Proc. Symp. Appl. Math., Vol. 57, AMS, Providence 1999, p. 180
  • 6. K. Sobczyk, Stochastic Differential Equations: with Applications to Physics and Engineering, Kluwer Academic Publishers, Dordrecht 1991, p. 416
  • 7. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Amsterdam 2006, p. 540
  • 8. Z. Szmydt, B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Kluwer Academic Publishers, Dordrecht 1992, p. 240
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv114n317kz
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