On the equivalence of a class of affine term structure models
Tóm tắt
In specifying a finite factor model for the term structure of interest rates, one usually begins by modeling the dynamics of the underlying factors. In most cases, this is sufficient to completely determine the term structure model. However, a point that is often overlooked is that seemingly different specifications of the factor dynamics may generate indistinguishable term structure models, in the sense that they produce pathwise identical bond prices. Consequently, it is important to be able to determine, at the level of factor dynamics, the conditions under which the models they generate are indistinguishable. In the case of time-homogeneous affine term structure models (ATSMs), such conditions were first described in Dai and Singleton (J Finance 55:1943–1978, 2000). In this paper, we formalize and extend their results to a class of time-inhomogeneous ATSMs, and obtain a simple method for determining the indistinguishability of these models in terms of the underlying factor dynamics.
Tài liệu tham khảo
Björk, T., Hyll, M.: On the inversion of the yield curve. Working Paper, Stockholm School of Economics (2000)
Björk, T., Svensson, L.: On the existence of finite dimensional realizations for nonlinear forward rate models. Math Financ 11, 205–243 (2001)
Brigo, D., Mercurio, F.: A deterministic-shift extension of analytically tractable and time-homogeneous short-rate models. Financ Stoch 5, 369–387 (2001)
Chen, R., Scott, L.: Pricing interest rate options in a two-factor Cox–Ingersoll–Ross model of the term structure. Rev Financ Stud 5, 613–636 (1992)
Cheridito, P., Filipović, D., Kimmel, R.: A note on the Dai–Singleton canonical representation of affine term structure models. Working paper, Fisher College of Buiness, The Ohio State University (2006)
Cox, J., Ingersoll, J., Ross, S.: A theory of the term structure of interest rates. Econometrica 53, 385–407 (1985)
Dai, Q., Singleton, K.: Specification analysis of affine term structure models. J Financ 55, 1943–1978 (2000)
Duffie, D., Kan, R.: A yield factor model of interest rates. Math Financ 6, 379–406 (1996)
Filipović, D., Teichmann, J.: On the geometry of the term structure of interest rates. Proc R Soc Lond Ser A 460, 129–167 (2004)
Heath, D., Jarrow, R., Morton, A.: Bond pricing and the term structure of interest rates: a new methodology for contingent claim valuation. Econometrica 60, 77–105 (1992)
Hull, J., White, A.: Pricing interest rate derivative securities. Rev Financ Stud 3, 573–592 (1990)
Kwon, O.: Short rate extensions of time-homogeneous affine term structure models. Working Paper, Discipline of Finance, The University of Sydney (2004)
Kwon, O.: Mean reversion level extensions of time-homogeneous affine term structure models. Appl Math Financ 14, 291–302 (2007)
Kwon, O., Lai, K.: Moduli space for Gaussian term structure models with finite dimensional realizations. Working Paper, Discipline of Finance, The University of Sydney (2006)
Longstaff, F., Schwartz, E.: Interest rate volatility and the term structure: a two-factor general equilibrium model. J Financ 47, 1259–1282 (1992)
Rotman, J.: An introduction to the theory of groups. Springer, New York (1995)
Vasic̆ek, O.: An equilibrium characterisation of the term structure. J Financ Econ 5, 177–188 (1977)