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A comparison of multi-factor term structure models for interbank rates

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Abstract

In this paper, we present a robust predictive comparison of several continuous-time multi-factor models in the context of interbank rates. Recognizing the specific dynamics of the short-term segment of the yield curve, we examine the U.S. money market by extending two continuous-time frameworks with different factor structures, the Chan-Karolyi-Longstaff-Sanders (CKLS) model and the arbitrage-free dynamic Nelson-Siegel (AFDNS) model. A battery of formal forecasting accuracy tests is employed to select a subset of superior predictive models. Despite a better goodness-of-fit measure, additional factors improve the forecasting performance only for the CKLS family. With implications for monetary policy formulation, we found evidence of two separate maturity segments as the three-factor AFDNS and the five-factor CKLS models outperform parsimonious benchmarks in predicting the interbank rates for very short maturities. Our comparative forecasting results are re-confirmed with stronger out-of-sample performance for the five-factor CKLS model when the post global financial crisis sub-sample is analyzed.

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Notes

  1. Joslin et al. (2013) differentiates between macro and yield-based models of the term structure of interest rates.

  2. https://www.ssga.com/investment-topics/environmental-social-governance/2019/05/what-happens-when-libor-is-phased-out.pdf.

  3. Some of the classical models nested in the CKLS general framework, such as Cox, Ingersol, and Ross (1985), and Brennan and Schwartz (1980), are non-Gaussian. To estimate them, Nowman (1997) employs their Gaussian approximations to obtain quasi-ML estimates.

  4. Sharef and Filipovic (2004) propose another four-factor arbitrage DNSS model by assuming square root processes as in the CIR model instead of Ornstein–Uhlenbeck processes for the state variables.

  5. The Kalman filter estimation approach in the context of AFDNS is presented in detail in Christensen et al. (2007).

  6. For the four-factor CKLS model, we used the first four maturities of the LIBOR curve that are available. The reason for not including the one-year LIBOR rate in the initial four-factor CKLS specification is based on the possibility of producing one-year maturity rates from other financial products such as Eurodollar futures and one-year swaps.

  7. To avoid the long-term impact of the GFC on the forecasting performance of the models, one could employ different techniques based on non-parametric models such as weighted historical simulation where different weights are given to different age data, more weight is given to more recent data, and less weight to more distant data.

  8. Because of space constraints, we only present the results for the SPA test while the results for the White (2000) reality check are available from the authors upon request.

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Funding

Funding was provided by EDHEC Business School.

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Authors and Affiliations

  1. EDHEC Business School, 06202, Nice Cedex 3, France

    Frank J. Fabozzi

  2. Yale School of Management, 165 Whitney Ave, New Haven, CT, 06511, USA

    Francesco A. Fabozzi

  3. Kent Business School, University of Kent, Park Wood, Canterbury, CT2 7FS, UK

    Diana Tunaru

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  1. Frank J. Fabozzi
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  2. Francesco A. Fabozzi
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Correspondence to Frank J. Fabozzi.

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Fabozzi, F.J., Fabozzi, F.A. & Tunaru, D. A comparison of multi-factor term structure models for interbank rates. Rev Quant Finan Acc 61, 323–356 (2023). https://doi.org/10.1007/s11156-023-01147-2

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