Post date: 06-Mar-2015 08:05:14
EDIT: Third Lecture 1 APRILE 2015, ore 14.30, Sala Riunioni Primo Piano
11-18 MARZO 2015, ore 11.00, Sala Riunioni Primo Piano
Relatore: Prof. Ernesto Salinelli, UPO, DiSEI
Titolo: How to spend ten years chasing three eigenvectors
Abstract:
It has been empirically observed that correlation matrices of interest rates have the first three eigenvalues
which are simple and their corresponding eigenvectors, called shift, slope and curvature (SSC) respectively,
with elements presenting changes of sign and monotonicity in a regular way. In two lectures we illustrate
problems, tools and results that have accompanied the efforts of the author and some co-authors during ten
years in order to explain and justify the presence of SSC in terms of some properties characterizing the
considered correlation matrices.
The outline is the following:
First lecture (11/03/2015): Yield curves and random vectors, properties of interest rates correlations, factor
models and Principal Component Analysis, Formal definition of SSC, Total positivity.
Second lecture (18/03/2015): some models of interest rates and SSC: Exponential and Schoenmakers-Coffey
models, Testing total positivity, Correlations of interest rates are TP₂.
Third lecture (01/04/2015): Testing total positivity, Correlations of interest rates are TP₂.