Abstract
We develop a two-factor model for the short-term interest rate that incorporates additional randomness in both the drift and diffusion components. In particular, the model nests stochastic volatility and stochastic central tendency, and therefore provides a medium for testing the overall importance of both factors. The randomness in the drift and diffusion terms is governed by a hidden Markov chain. The likelihood function is determined through an iterative procedure and maximum likelihood estimates are obtained via numerical maximization. This process allows likelihood ratio testing of nested restrictions. These tests show that stochastic volatility is more important than stochastic central tendency for describing the short rate dynamics.
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- 1.
Moving to daily observations may also introduce too much serial correlation, which may lead to inconsistent estimators.
- 2.
For robustness we repeated the analysis for the shorter time period from May 1990 to December 2004 using 3-month T-bill rates, 3-month LIBOR rates, and 1-month LIBOR rates, and although the parameters differed substantially from the longer period, the findings were generally similar. The only noteworthy differences were that β 1 was significantly less than zero, ruling out a unit root in each case, and for the Canadian short rates, serial correlation in the residuals was no longer present. Data for the LIBOR rates was obtained at the British Bankers’ Association website.
- 3.
For robustness, the complete analysis was repeated for a 3-state Markov chain and the results were qualitatively the same: Stochastic central tendency was important only when compared to the 1-factor model. It was unimportant when compared with a stochastic volatility model.
- 4.
For robustness, we further restricted the stochastic volatility models by requiring all drift parameters to be 0. Such restrictions had little effect on the log-likelihoods and the LR statistics were all less than 0.4.
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Wilson, C.A., Elliott, R.J. (2014). Stochastic Volatility or Stochastic Central Tendency: Evidence from a Hidden Markov Model of the Short-Term Interest Rate. In: Mamon, R., Elliott, R. (eds) Hidden Markov Models in Finance. International Series in Operations Research & Management Science, vol 209. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7442-6_2
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DOI: https://doi.org/10.1007/978-1-4899-7442-6_2
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