##
**Drift and diffusion function specification for short-term interest rates.**
*(English)*
Zbl 1254.91733

Summary: Various stochastic differential equation models for short rates \((r_{t})\) are proposed, where the change \((\Delta r_{t}=r_{t} - r_{t - 1})\) is modeled as a sum of drift and diffusion terms depending on \(r_{t - 1}\). These models, however, have some shortcomings. First, the same model may not apply to all countries. Second, the drift and diffusion may depend not only on \(r_{t - 1}\) but also on further lags. Third, not just the own lagged rates, but also other countries’ rates may matter. These questions are empirically analyzed for six major countries with the following findings. First, there are considerable differences in drift and diffusion across the countries. Second, the drift and diffusion often depend on \(r_{t - 2}\) (and \(r_{t - 3}\)). Third, foreign rates exert substantial effects.

### MSC:

91G30 | Interest rates, asset pricing, etc. (stochastic models) |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

62H10 | Multivariate distribution of statistics |

PDF
BibTeX
XML
Cite

\textit{M.-J. Lee} and \textit{W.-J. Li}, Econ. Lett. 86, No. 3, 339--346 (2005; Zbl 1254.91733)

### References:

[1] | Ahn, D.H.; Gao, B., A parametric nonlinear model of term structure dynamics, Review of financial studies, 12, 721-762, (1999) |

[2] | Aït-Sahalia, Y., Nonparametric pricing of interest rate derivative securities, Econometrica, 64, 527-560, (1996) · Zbl 0844.62094 |

[3] | Aït-Sahalia, Y., Testing continuous-time models of the spot interest rate, Review of financial studies, 9, 385-427, (1996) |

[4] | Chan, K.C.; Karolyi, G.A.; Longstaff, F.A.; Sanders, A.B., An empirical comparison of alternative models of the short-term interest rate, Journal of finance, 47, 1209-1228, (1992) |

[5] | Chapman, D.A.; Pearson, N.D., Is the short rate drift actually nonlinear?, Journal of finance, 55, 355-388, (2000) |

[6] | Künsch, H.R., The jackknife and the bootstrap for general stationary observations, Annals of statistics, 17, 1217-1261, (1989) · Zbl 0684.62035 |

[7] | Lahiri, S.N., Theoretical comparisons of block bootstrap methods, Annals of statistics, 27, 386-404, (1999) · Zbl 0945.62049 |

[8] | Overbeck, L.; Rydén, T., Estimation in the Cox-ingersoll-ross model, Econometric theory, 13, 430-461, (1997) |

[9] | Stanton, R., A nonparametric model of the term structure dynamics and the market price of interest rate risk, Journal of finance, 52, 1973-2002, (1997) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.