Information, interest rates, and geometry

The characterisation of interest-rate dynamics requires the understanding of the interest-rate term structure (dependencies of the bond price on different maturities). As such, interest-rate modelling amounts to the modelling of the random dynamics of a smooth curve, known as the "yield curve". A priori there is no structure on the space of yield curves to allow for an elegant mathematical characterisation, but it turns out that there is a remarkable correspondence between an yield curve and a probability density function. The dynamics of interest-rate term structure can then be represented as a measure-valued process, and the latter allows for the powerful method of information geometry to identify useful quantities like the separation of two interest rate markets. One can, furthermore, ask where does the random dynamics of interest rates emerge from? This is given by the flow of information in financial markets concerning various economic factors such as the liquidity risk. The dynamics of the term-structure density function can then be seen as the result of an optimum filter, calculated by the market. We can therefore model the flow of information explicitly and derive interest rate dynamics, seen as an emergent phenomena.
[1] Brody, D.C. & Hughston, L.P. (2001) Interest rates and information geometry. Proceedings of the Royal Society London A457, 1343-1364.
[2] Brody, D.C. & Friedman, R.L. (2009) Information of interest. Risk Magazine, December, 105-110 (reprinted in: Life & Pensions, February 2010, 35-40).