Narrow Results

Motivated by stylized statistical properties of interest rates, we propose a modeling approach in which the forward rate curve is described as a stochastic process in a space of curves. After decomposing the movements of the term structure into the variations of the short rate, the long rate and the deformation of the curve around its average shape, this deformation is described as the solution of a stochastic evolution equation in an infinite dimensional space of curves. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates, the structure of principal components of forward rates and their variances. In particular we show that a flat, constant volatility structures already captures many of the observed properties. Finally, we discuss parameter estimation issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.

The defaultable term structure is modeled using stochastic differential equations in Hilbert spaces. This leads to an infinite dimensional model, which is free of arbitrage under a certain drift condition. Furthermore, the model is extended to incorporate ratings based on a Markov chain.

In this paper, we show how to construct dynamic forward rate models in terms of exogenously specified eigenfunctions (or factor loadings). We also show how to link forward rate models with different number of driving Brownian motions to each other in a way consistent with the implied eigenfunctions. Finally, we discuss how to best parameterize the models in the sense of maximizing the number of free parameters for a given set of eigenfunctions.

There is a huge literature on whether forward rates of interest provide unbiased estimates of future interest rates. In most studies econometric evidence is presented which is apparently inconsistent with market efficiency; but more rarely is the economic, as opposed to statistical, significance of deviations from efficiency investigated. This paper uses accurate, up-to-date information on short term money market rates, from a common source, for all the major economies to assess efficiency and profit opportunities. The economic significance of deviations from the conditions required for efficiency are assessed by testing various trading rules.

The paper explores the potential to make profits from money market transactions based on simple rules derived from econometric analysis of the relation between current and future interest rates. We find that in many cases there are systematic divergences between forward rates and future spot interest rates for various currencies quoted on the London interbank market.