Revisiting Elastic String Models of Forward Interest Rates

Paper: arXiv 2403.18126

Abstract

Twenty five years ago, several authors proposed to describe 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 around 1% and with only one adjustable parameter, the value of which being very stable across the last three decades. 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 on the order of 30 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 behavioral Finance literature (Farmer and Geanakoplos, 2009).

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced field theory with a functional action integral and Langevin dynamics (math complexity high), while also providing a comprehensive 30-year backtest (1994-2023) with specific metrics like error percentages and cross-tenor propagation times (empirical rigor high).

Research Flowchart

  flowchart TD
  A["Research Goal<br>Revisit elastic string model for<br>Forward Rate Curve micro-foundation"] --> B["Methodology<br>Stiff elastic string field theory<br>+ Self-referential market forces"]
  B --> C["Data Input<br>US FRC data 1994-2023<br>across multiple maturities"]
  C --> D["Computational Process<br>Calibrate 1 free parameter<br>Fit correlation structure"]
  D --> E{"Analysis"}
  E --> F["Outcome 1<br>Accurate correlation reproduction<br>Error ~1%, 1 stable parameter"]
  E --> G["Outcome 2<br>Epps effect reproduced<br>Cross-tenor propagation ~30 min"]
  E --> H["Outcome 3<br>Sub-linear perceived time<br>Compatible with hyperbolic discounting"]

Cited References (763)

1. FRB : FEDS Abstract 2006-28
2. Elliptical and Related Distributions (2007) — link
3. Stochastic Processes in Physics and Chemistry (2007) — link
4. Test
5. Multi-Armed Bandit.Pdf
6. Bank Network\ldots (4) - JupyterLab
7. Test
8. Ecb.Wp2806\textasciitilde 38d51fae59.En.Pdf

0 of 763 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.