Modelling of Short Term Interest Rate Based on Fractional Relaxation Equation

• Authors: K. Jaworska
• Languages of publication: 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.

Keywords

EN

89.65.Gh

Discipline

• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2008
• Volume: 114
• Issue: 3
• Pages: 613-618

Dates

published

2008-09

received

2007-11-22

Contributors

author

K. Jaworska

• Institute of Mathematics and Cryptology, Military University of Technology, Kaliskiego 2, 00-908 Warszawa, Poland

References

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• 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

Identifiers

DOI

10.12693/APhysPolA.114.613