Positive Matrices and Derivative Models

Carlos Tolmasky
University of Minnesota 
Friday, September 27, 2019 - 5:30pm to 6:30pm
Vincent Hall 16

Principal components analysis has become widely used in a variety of fields. In finance and, more specifically, in the theory of interest rate derivative modeling, its use has been pioneered by R. Litterman and J. Scheinkman. Their key finding was that a few components explain most of the variance of treasury zero-coupon rates and that the first three eigenvectors represent level, slope and curvature changes on the curve. This result has been, since then, observed in various markets.Over the years, there have been several attempts at modeling correlation matrices displaying the observed effects as well as trying to understand what properties of the those matrices are responsible for the effect. Using recent results of the theory of positive matrices we characterize these matrices and, as an application, we shed light on some of the critiques to this methodology.Bio: http://mcfam.math.umn.edu/people/carlos-tolmasky