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An empirical comparison of continuous time models of the short term interest rate

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  • Turan G. Bali

Abstract

This article tests the performance of a wide variety of well‐known continuous time models—with particular emphasis on the Black, Derman, and Toy (1990; henceforth BDT) term structure model—in capturing the stochastic behavior of the short term interest rate volatility. Many popular interest rate models are nested within a more flexible time‐varying BDT framework that allows us to compare the models and find the proper specification of the dynamics of short rates. The empirical results indicate that the equilibrium models that do not allow the drift and diffusion parameters to vary over time and parameterize the volatility only as a function of interest rate levels overemphasize the sensitivity of volatility to the level of interest rate and fail to model adequately the serial correlation in conditional variances. On the other hand, the GARCH‐based arbitrage‐free models with time‐dependent parameters in the drift and diffusion functions define the volatility only as a function of unexpected information shocks and fail to capture adequately the relationship between interest rate levels and volatility. This study shows that the most successful models in capturing the dynamics of short term interest rates are those that introduce time‐dependent parameters to the short rate process and define the conditional volatility as a function of both the interest rate levels and the last period's unexpected news. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 777–797, 1999

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  • Turan G. Bali, 1999. "An empirical comparison of continuous time models of the short term interest rate," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 777-797, October.
  • Handle: RePEc:wly:jfutmk:v:19:y:1999:i:7:p:777-797
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    Cited by:

    1. Josheski Dushko & Apostolov Mico, 2021. "Equilibrium Short-Rate Models Vs No-Arbitrage Models: Literature Review and Computational Examples," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(3), pages 42-71, September.
    2. Yuh-Dauh Lyuu & Chi-Ning Wu, 2005. "On accurate and provably efficient GARCH option pricing algorithms," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 181-198.
    3. Sandy Suardi & O.T.Henry & N. Olekalns, "undated". "Equity Return and Short-Term Interest Rate Volatility: Level Effects and Asymmetric Dynamics," MRG Discussion Paper Series 0205, School of Economics, University of Queensland, Australia.

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