Term Structure Model of Interest Rates
A Literature Review
DOI:
https://doi.org/10.6981/FEM.202410_5(10).0001Keywords:
Term Structure Modeling; Nelson-Siegel Model; The Affine Term Structure Model.Abstract
Term structure modeling has enjoyed rapid growth during the last three decades. Given a large number of existing term structure models and a vast array of issues in the field, we attempt to provide a general overview of the most popular term structure of interest rate models. In order to understand different features of each model we classify by means of general characteristics from single-factor to multi-factor and forward rate based models. Each of these existing term structure models has its own advantages and disadvantages. We also highlight the recent advocated models in the literature: the Nelson-Siegel model, the affine and the quadratic arbitrage-free model.
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[1] Ahn D-H, Dittmar RF and Gallant RA.: Quadratic term structure models: theory and evidence, Review of Financial Studies, vol. 15 (2002), No.1, p.243–288.
[2] Backus, D., S. Foresi, and C. Telmer: Affine term structure models and the forward premium anomaly, Journal of Finance, vol. 56 (2001), p.279-304.
[3] Bjork, T. and B.J. Christensen: Interest rate dynamics and consistent forward rate curves, Mathematical Finance, vol. 9 (1999), No.4, p.323-348.
[4] Bliss, R.: Movements in the term structure of interest rates, Economic Review, Federal Reserve Bank of Atlanta, vol. 82 (1997a), p.16-33.
[5] Black F. and Karasinski P.: Bond and option pricing when short rates are lognormal, Financial Analysts Journal (1991), p.52-59.
[6] Brennan M.J. and Schwartz E. S.: A continuous time approach to the pricing of bonds, Journal of Banking and Finance, vol. 3(1979), p. 135-155.
[7] Brennan M.J. and Schwartz E. S.: An equilibrium model of bond pricing and a test of market efficiency, Journal of Financial and Quantitative Analysis, vol. 15 (1982), p. 907-929.
[8] Chen L.: Stochastic mean and stochastic volatility: a three factor model of the term structure of interest rates and its application to the pricing of interest rate derivatives, Blackwell publishers (1996).
[9] Christensen, J. H. E., F.X. Diebold and G..D. Rudebusch: The affine arbitrage-free class of Nelson-Siegel term structure models, American Economic Review, vol. 95 (2007), No.2, p.415-420.
[10] Christensen, J. H. E., F.X. Diebold and G..D. Rudebusch: An arbitrage-free generalized Nelson-Siegel term structure model, Econometrics Journal, vol.01 (2008), p.1-31.
[11] Cox, J., J. Ingersoll, and S. Ross: An Intertemporal General Equilibrium Model of Asset Prices, Econometrica, 53 (1985a), p.363-384.
[12] Cox, J., J. Ingersoll, and S. Ross: A Theory of the Term Structure of Interest Rates, Econometrica, 53 (1985b), p.385-406.
[13] Dai, Q., and K. Singleton: Specification Analysis of Affine Term Structure Models, Journal of Finance, vol. 55 (2000), p.1943-1978.
[14] Diebold, F. X. and C. Li: Forecasting the term structure of government bond yields, Journal of Econometrics, vol. 130 (2006), No.2, p.337-364.
[15] Diebold, F. X., Ji, L and Yue, V.: Global yield curve dynamics and interactions: A generalized Nelson-Siegel approach, working paper, University of Pennsylvania, (2007).
[16] Duffee, G.: Term Premia and Interest Rate Forecasts in Affine Models, working paper, University of California, Berkeley, (2000).
[17] Duffie, D. and R. Kan: A Yield-Factor Model of Interest Rates, Mathematical Finance, vol. 6 (1996), p.379-406.
[18] Duffie, D. and K. Singleton: An Econometric Model of the Term Structure of Interest Rates, Journal of Finance, vol.52 (1997), p.1287-1321.
[19] Feller: Two singular diffusion problems, Ann. Math., vol. 54 (1951), p. 173-181.
[20] Fong H.G and Vasicek O.A.: Omission impossible, Risk, vol. 5 (1992a), No.2, p.62-65.
[21] Fong H.G and Vasicek O.A.: Interest rate volatility as a stochastic factor, Gifford Fong Associates working paper, (1992b).
[22] Harrison, M., and D. Kreps: Martingales and Arbitrage in Multiperiod Security Markets, Journal of Economic Theory, vol.20 (1979), p.381-408.
[23] Heath, D., Jarrow, R. and Morton, A.: Bond pricing and the term structure of interest rates: a discrete time approximation, Journal of Financial and Quantitative Analysis, vol. 25(1990a), p.419–40.
[24] Heath, D., Jarrow, R. and Morton, A.: Contingent claim valuation with a random evolution of interest rates, Review of Futures Markets, vol. 9(1990b), p.54–76.
[25] Heath, D., Jarrow, R. and Morton, A.: Bond pricing and the term structure of interest rates: a new Methodology, Econometrica, 60(1992), p.77–105.
[26] Ho, T.S.Y. and Lee, S.B.: Term structure movements and the pricing of interest rate contingent claims, Journal of Finance, vol.41 (1986), p.1011–29.
[27] Hull, J. and White, A.: Pricing interest rate derivative securities’, Review of Financial Studies, vol. 3(1990), p.573–92.
[28] Hull, J. and White, A. : One-factor interest rate models and the valuation of interest rate derivative securities, Journal of Financial and Quantitative Analysis, vol. 28 (1993), p.235–254.
[29] Hull J. and White A: Numerical procedures for implementing term structure models I: single-factor models, Journal of Derivatives, Autumn (1994a), p.7-16.
[30] Hull J. and White A: Numerical procedures for implementing term structure models I: two-factor models, Journal of Derivatives, Winter (1994b), p.37-49
[31] Jamshidian F: Forward Induction and construction of yield curve diffusion models, Journal of Fixed Income, vol.1 (1991), p.62-74
[32] Kim, D.H and Jonathan H. Wright: An arbitrage-free three-factor term structure model and the recent behavior of long-term yields and distant-horizon forward rates, Finance and Economics Discussion Series, Working paper (2005), 2005-33.
[33] Leippold M, Wu L: Design and estimation of quadratic term structure models, European Finance Review, vol.7 (2003), p.47–73.
[34] Leippold M, Wu L: Design and estimation of multi-currency quadratic models’, Review of Finance, vol.11 (2007), p.167–207.
[35] Longstaff, F. and E. Schwartz: Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model, Journal of Finance, vol.47 (1992), p.1259-1282.
[36] Nelson, C.R, and A.F. Siegel: Parsimonious modeling of yield curves, The Journal of Business, vol. 60(1987), No.4, p.473-489.
[37] Vasicek, O: An equilibrium characterization of the term structure, Journal of Financial Economics, vol.5 (1977), p.177-88.
[38] Chi Xie, Xiongwei Wu: Interest rate term structure model under jump-diffusion process, Research on quantitative economy and technical economy, vol.11(2001). (In Chinese)
[39] Qian Li, Yijing Liao: An empirical study on the term structure of inter-bank treasury bond interest rate based on Nelson-Siegel-Svensson model, Journal of Liaoning University of Technology Science (social science edition), vol.04 (2019). (In Chinese)
[40] A principal component analysis is a statistical technique that identifies the best factors from historical yields, where the term best is in the sense of the two conditions: 1) the factors ought to explain a very large proportion of the variation of the yields of bonds at various horizons; 2) the factors should be independent of each other.
[41] Gaussian process and square-root process are the best known examples of affine diffusions. Gaussian process has a constant volatility, while the square-root processes introduce conditional heteroskedasticity by allowing the volatility function to depend on the state variables.
[42] Within the family of Duffie and Kan affine term structure model, there is a trade-off between flexibility in modeling the conditional correlations and volatilities of the risk factors. This trade-off is formalized by their classification of N-factor affine family into N + 1 non-nested subfamilies of models. Vasicek (1977), Chen (1996), and Cox, Ingersoll and Ross(1985) models are classified into distinct subfamilies of the affine models.
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