Ab initio yield curve dynamics

Abstract

We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success of the Nelson Siegel approach to fitting static yield curves and the empirically observed modal structure of yield curves. A practical numerical implementation of this equation of motion is found by using the Karhunen-Lòeve expansion and Galerkin's method to formulate a reduced-order model of yield curve dynamics.Key words: Bond, interest rate, dynamics, Fisher information, yield curve, term structure, principal-component analysis, proper orthogonal decomposition, Karhunen-Lòeve, Galerkin, Fokker-Planck. PACS: 89.65. Gh, 89.70.+c Yield curves are remarkable in that the fluctuations of these structures can be explained largely by a few modes and that the shape of these modes is largely independent of the market of origin: a combination of parsimony and explanatory power rarely seen in financial economics. While these modes play a fundamental role in fixed-income analysis and risk management, both the origin of this modal structure and the relationship between this modal structure and a formal description of yield curve dynamics remain unclear. The purpose of this letter is to show that this modal structure is a natural consequence of the information structure of the yield curve and that this information structure, in turn, implies an equation of motion for yield curve dynamics.1 We thank Prof. Ewan Wright for helpful discussions and encouragement.