Long-horizon yield curve projections: comparison of semi-parametric and parametric approaches

Abstract

Two methods for evolving forward the yield curve are evaluated and contrasted within a Monte Carlo experiment: one is originally presented by Rebonato et al. (2005) and the other by Bernadell et al. (2005). A detailed account for how to implement the models is also presented. Results suggest that the two techniques are complementary and able to capture important cross-sectional and time-series properties of observed yield curve data. Our results are of interest to practitioners in the financial markets as well as central banks who need accountable and history consistent procedures for generating long-term yield curve forecasts.

Notes

¹ Rebonato et al. (2005) show that some statistically plausible term structure models produce future yield curves that fail to resemble anything ever observed in the real world. This ‘optical’ analysis is a useful pointer to uncover deeper statistical inadequacies of the naive modelling approach.

² The term ‘explicitly regime-switching’ refers to those models where regime switching is explicitly built into the model itself. As we shall see, however, also the RMJBN model displays features consistent with regime-switching, even if this feature is not imposed a priori from the outset.

³ The term ‘reduced form’ is often used in the credit-derivatives literature to denote models that dispense with the specification of the evolution of the form assets, and deal directly with the probability of defualt. We do not imply such a technical meaning in this article, but we still refer to models that by-pass a higher-level description (in our case, of the real-world dynamics and of the investors’ preferences) and directly model the risk-neutral measure.

⁴ The maturities observed in the RMJBN dataset are 3m, 6m, 1y, 2y, 5y, 10y, 20y and 30y.

⁵ It must be emphasized that the statistical validity of the approach does not hinge on the correctness of the interpretation of the springs as describing the action of the pseudo-arbitrageurs. Even if this ‘picture’ is not correct, Rebonato et al. (2005) show that the springs correctly recover important features of the real-world yield curves.

⁶ The implementation of the regime-switching model relies on Hamilton (1994, Ch. 22) and its setup builds implicitly on Diebold and Rudebusch (1996).

⁷ These choices are based on results from Evans (2003) and Bernadell et al. (2005).

⁸ Here we deviate slightly from RMJBN by introducing a minimum block length and by using a slightly higher maximum number for the length of the block.

⁹ Experiments show that there is no qualitative difference between results derived from daily and monthly data. However, a significant difference in calculation time is observed. On a PC (3.2 GHZ, 1 MB RAM), it takes approximately 10 min to obtain convergence when 235 time series of monthly observations are used and more than 3 h when 4700 daily observations are used.

¹⁰ However, these numbers seems to be biased when compared to estimates based on the full sample, i.e. the original data covering 1986–2004. Here the occurence frequency of the regimes are ≈32, 40 and 28% for main, steep and flat, respectively.

¹¹ We use data similar to that used by Bernadell et al. (2005).

¹² It is worth remembering that Bernadell et al. (2005) use a model that is slightly different from our setup in that their transition probability matrix is contingent on macroeconomic variables. Also, they apply a data transformation which we do not. Despite these differences in model setup and data, the estimated parameters in the two studies are very similar.

¹³ Note that the Nelson–Siegel form reverts the sign of the slope factor; hence a negative slope factor represents an upward sloping yield curve and, conversely, a positive slope factor represents an inversely shaped yield curve.

¹⁴ Note that the parameter estimates reported by Bernadell et al. (2005) correspond to the transformed data, which reportedly ensures that the slope of the yield curve becomes independent from the yield curve level. To make their parameter estimates comparable to ours, we have ‘unscaled’ their estimates by multiplying them by the average of the yield curve level, as suggested in Table 2 of Bernadell et al. (2005)