Revisiting Elastic String Models of Forward Interest Rates

Abstract

Twenty five years ago, several authors proposed to model the forward interest rate curve (FRC) as an elastic string along which idiosyncratic shocks propagate, accounting for the peculiar structure of the return correlation across different maturities. In this paper, we revisit the specific "stiff'' elastic string field theory of Baaquie and Bouchaud (2004) in a way that makes its micro-foundation more transparent. Our model can be interpreted as capturing the effect of market forces that set the rates of nearby tenors in a self-referential fashion. The model is parsimonious and accurately reproduces the whole correlation structure of the FRC over the time period 1994-2023, with an error below 2%. We need only two parameters, the values of which being very stable except perhaps during the Quantitative Easing period 2009-2014. The dependence of correlation on time resolution (also called the Epps effect) is also faithfully reproduced within the model and leads to a cross-tenor information propagation time of 10 minutes. Finally, we confirm that the perceived time in interest rate markets is a strongly sub-linear function of real time, as surmised by Baaquie and Bouchaud (2004). In fact, our results are fully compatible with hyperbolic discounting, in line with the recent behavioural literature (Farmer and Geanakoplos, 2009).