Abstract
Since the seminal paper of Duffie and Kan (1996), most empirical research on the term structure of interest rates has focused on a class of linear models, generally referred to as “affine term structure models.” Since these models produce such a closed-form solution for the entire yield curve, they become very tractable in empirical applications. Nonlinearity can be introduced into dynamic models of the term structure of interest rates either by generalizing the affine specification to a quadratic form or by including a Poisson jump component as an additional state variable. In our paper, we survey some recent studies of dynamic models of the term structure of interest rates that incorporate Markov regimes shifts. We not only summarize an early literature of regime-switching models that mainly focus on the short-term interest rate, but also the recent studies considering regime-switching models in discrete-time and continuous-time, respectively.
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Notes
- 1.
OAPEC is an abbreviation for Organization of Arab Petroleum Exporting Countries consisting of the Arab members of OPEC plus Egypt and Syria.
- 2.
Engle (1982) shows that a possible cause of the leptokurtosis in the unconditional distribution is conditional heteroskedasticity.
- 3.
- 4.
Markov property argues that the process of s t depends on the past realizations only through s t − 1.
- 5.
See Kim and Nelson (1999).
- 6.
Garcia and Perron (1996) employs Hamilton’s (1989) regime-switching model to explicitly account for regime shifts in an autoregressive model with three-state regime-switching mean and variance.
- 7.
For simplicity, the following analysis is based only on one industry. We thus omit the symbol i.
- 8.
The following derivations are mainly from Shen (1994).
- 9.
f(.) and p(.) denote the continuous and discrete density function, respectively.
- 10.
In the case of stochastic volatility, affine models assume that the product of the market price of risk and the volatility term is a linear function of the state variable X t . In other words, it is assumed that, under the risk-neutral probability measure, X t follows a linear mean-reverting process
- 11.
Of course, some regularity conditions need to be imposed on the parameters so that the term inside the square root is non-negative and the process is well defined. See Dai et al. (2006) for more details.
- 12.
This is the approximation used in Bansal and Zhou (2002).
- 13.
See Last and Brandt (1995) for detailed discussion on marked point process, stochastic intensity kernel, and related results.
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Nieh, CC., Wu, S., Zeng, Y. (2010). Regime Shifts and the Term Structure of Interest Rates. In: Lee, CF., Lee, A.C., Lee, J. (eds) Handbook of Quantitative Finance and Risk Management. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77117-5_72
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