Approximation of Distributions of Treasury Bill Yields and Interbank Rates by Means of α-stable and Hyperbolic Distributions

  • Witold Szczepaniak
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


In this paper α-stable and hyperbolic distributions are presented and proposed as alternatives to the normal distribution in approximation of treasury bill yields and interbank rates distributions.


Term Structure Model Interest Rate Model Hyperbolic Distribution Levy Process Interbank Rate 
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  1. BARNDORFF-NIELSEN, O.E. (1977): Exponentially decreasing distributions for the logarithm of practicle size. Proceedings of the Royal Society A 353, 401–419.CrossRefGoogle Scholar
  2. BARNDORFF-NIELSEN, O.E. (1995): Normal inverse Gaussian processes and the modeling of stock returns, Research Reports No. 300, University of Aarhus.Google Scholar
  3. BARNDORFF-NIELSEN, O.E. (1998): Processes of normal inverse Gaussian type. Finance and Stochastics 2, 41–68.MATHMathSciNetCrossRefGoogle Scholar
  4. BAS, B. and DAS, S. (1996): Analytical approximation of the term structure for jump-diffusion processes: a numerical analysis. Journal of Fixed Income, June, 78–86.Google Scholar
  5. BJÖRK, T., KABANOV, Y, and RUNGGALDIER, W. (1997): Bond market structure in the presence od marked point processes. Mathematical Finance 7, 211–239.MathSciNetCrossRefMATHGoogle Scholar
  6. BLÆSILD, P. (1999): Generalized hyperbolic and generalized inverse Gaussian distributions, Working Paper, University of Aarhus.Google Scholar
  7. DAS, S. (2002): The surprise element: jumps in interest rate models. Journal of Econometrics, 106, 27–65.MATHMathSciNetCrossRefGoogle Scholar
  8. EBERLEIN, E. and KELLER, U. (1995): Hyperbolic distributions in finance. Bernoulli 1, 281–299.CrossRefMATHGoogle Scholar
  9. EBERLEIN, E., KELLER, U, and PRAUSE, K. (1998): New insights into smile, mispricing and value and risk: the hyperbolic model. Journal of Business, 71, 371–405.CrossRefGoogle Scholar
  10. EBERLEIN, E. and ÖZKAN, F. (2002): The Lévy LIBOR Model, Working Paper, University of Freiburg.Google Scholar
  11. EBERLEIN, E. and RAIBLE, S. (1999): Term structure models driven by general Levy processes. Mathematical Finance 9, 31–53.MathSciNetCrossRefMATHGoogle Scholar
  12. EMBRECHTS, P., KLÜPPELBERG, C, and MIKOSCH, T. (1997): Extremal events for insurance and finance. Springer-Verlag, Berlin Heidelberg.MATHGoogle Scholar
  13. FAMA, E. (1965): The behavior of stock market prices. Journal of Business, 38, 34–105.CrossRefGoogle Scholar
  14. GLASSERMAN, P. and KOU, S. (1999): The term structure models of simple forward rates with jump risk, Working Paper, Columbia University.Google Scholar
  15. GLASSERMAN, P. and MERENER, N. (2001): Cap and swaption approximation in LIBOR Market Models with jumps, Working Paper, Columbia University.Google Scholar
  16. JOHANNES, M. (2001): The statistical and economic role of jump in continuous-time interest rate models, Working Paper, Graduate School of Business Columbia University.Google Scholar
  17. MANDELBROT, B. (1963): The Variation of Certain Speculative Prices. Journal of Business, 36, 394–419.CrossRefGoogle Scholar
  18. MITTNIK, S. and RACHEV, S. (2001): Stable Paretian models in finance, Wiley, New York.Google Scholar
  19. NOLAN, J. (1999): Maximum likelihood estimation and diagnostics for stable distributions, Working Paper, American University, Washington.Google Scholar
  20. PRAUSE, K. (1999): The generalized hyperbolic model: estimation, financial derivatives and risk measures, Ph.D. dissertation, University of Freiburg.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2005

Authors and Affiliations

  • Witold Szczepaniak
    • 1
  1. 1.Department of Financial Investments and InsuranceWroclaw University of EconomicsWroclawPoland

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