Stiff Field Theory of Interest Rates and Psychological Future Time

15 March 2004

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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 normalised 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.

Authors

Belal Baaquie , Jean-Philippe Bouchaud