How to spend ten years chasing three eigenvectors

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.