Interest rates and information geometry (Q2748083)

It is shown that, in the context of term structure modelling, the derivative of the discount function with respect to the time left until maturity gives rise to a probability density (this is due to the positivity of interest rates). The density functions associated with a given family of term structures can be mapped to a suitable Hilbert space. The resulting metrical geometry can then be used to analyze the relationship of yield curves to one another. Then it is shown that the general arbitrage-free yield-curve dynamics is representable as a process taking values in the convex space of smooth density functions on the real line. This, in turn, implies that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. As a consequence the dynamical laws of the first moment and the second central moment of an admissible, arbitrage-free term structure are derived.