Some Results on Correlation Matrices for Interest Rates

In this paper we systematize and develop some theoretical results about shift, slope and curvature for correlations matrices of interest rates. We provide a general investigation on the relations among some standard features of correlation models for interest rates and the existence of shift, slope...

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Bibliographic Details
Published in:Acta applicandae mathematicae 2011-09, Vol.115 (3), p.291-318
Main Authors: Salinelli, Ernesto, Sgarra, Carlo
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Computational Mathematics and Numerical Analysis
Correlation
Correlation analysis
Curvature
Eigenvectors
Interest rates
Inverse problems
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Matrices
Matrix methods
Partial Differential Equations
Principal components analysis
Probability Theory and Stochastic Processes
Studies
Vectors (mathematics)
Yield curve
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Summary:In this paper we systematize and develop some theoretical results about shift, slope and curvature for correlations matrices of interest rates. We provide a general investigation on the relations among some standard features of correlation models for interest rates and the existence of shift, slope and curvature. Our results show how their presence, excluding some peculiar behavior strictly related to low dimensions, can not be directly connected to the usual assumptions on the interest rates correlations structure. We provide some estimates of the distance between a shift and the vector, named pure shift, having all entries equal. We prove also that in a two-factor framework shift and slope are sufficient to justify the usual properties of correlations between rates.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-011-9622-x