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Time-dependent diffusion models for term structure dynamics. (English) Zbl 1065.62177

Summary: In an effort to capture the time variation on the instantaneous return and volatility functions, a family of time-dependent diffusion processes is introduced to model the term structure dynamics. This allows one to examine how the instantaneous return and price volatility change over time and price level. Nonparametric techniques, based on kernel regression, are used to estimate the time-varying coefficient functions in the drift and diffusion. The newly proposed semiparametric model includes most of the well-known short-term interest rate models such as those proposed by J. C. Cox, J. E. Ingersoll and S. A. Ross [Econometrica 53, 385–467 (1985)] and K. C. Chan et al. [J. Finance 47, 1209–1227 (1992)]. It can be used to test the goodness-of-fit of these famous time-homogeneous short rate models.
The newly proposed method complements the time homogeneous nonparametric estimation techniques of R. Stanton [ibid. 52, 1973–2002 (1997)] and J. Fan and Q. Yao [Biometrika 85, 645–660 (1998; Zbl 0918.62065)], and is shown through simulations to truly capture the heteroscedasticity and time-inhomogeneous structure in volatility. A family of new statistics is introduced to test whether the time-homogeneous models adequately fit interest rates for certain periods of the economy. We illustrate the new methods by using weekly three-month treasury bill data.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
62G08 Nonparametric regression and quantile regression
62M05 Markov processes: estimation; hidden Markov models
62G07 Density estimation
62G10 Nonparametric hypothesis testing

Citations:

Zbl 0918.62065
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