## 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

### Keywords:

short rate; diffusion; spatial correlation
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### References:

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