"Stiff" Field Theory of Interest Rates and Psychological Future Time

Abstract

The simplest field theory description of the multivariate statistics of forward rate variations over time and maturities, involves a quadratic action containing a gradient squared rigidity term. However, this choice leads to a spurious kink (infinite curvature) of the normalized correlation function for coinciding maturities. Motivated by empirical results, we consider an extended action that contains a squared Laplacian term, which describes the bending stiffness of the FRC. With the extra ingredient of a `psychological' future time, describing how the perceived time between events depends on the time in the future, our theory accounts extremely well for the phenomenology of interest rate dynamics.