Modeling the Term Structure of Interest Rates: Where Do We Stand?
No-arbitrage term structure models are becoming increasingly important to policy makers and practitioners alike. Several factors justify this trend. First, modeling progress has been tremendous over the last years, allowing a much better fit of actual yield curve dynamics and increased model realism (see Dai and Singleton (2002a,b)). Second, increases in computing power allow the efficient panel estimation of term structure models. Given that term structure models have implications for both the cross-section and time series dimension of yields, panel estimation techniques are to be preferred over either crosssection or time series techniques. Third, term structure models have recently been extended in ways that are of direct interest to policy makers. Example given, Dewachter and Maes (2001) model the international term structure of interest rates, taking into account the role of the exchange rate in a no-arbitrage economy, while amongst others Hördahl et al. (2002) and Dewachter et al. (2002) jointly model the term structure of interest rates with the dynamics of macroeconomic variables. The latter approach allows to study (i) the driving factors behind the term structure and the risk premia in terms of clearly interpretable macroeconomic variables and their determinants, and (ii) the effects of monetary policy on the term structure of interest rates and macroeconomic variables within a consistent no-arbitrage framework.
This paper provides an introduction to the mathematical models that describe the shape of the term structure of interest rates across time. In essence, all these so-called term structure models are driven by the assumption that arbitrage opportunities are absent. The intuitive concept of absence of arbitrage can be linked directly to the existence of a pricing kernel and a risk neutral probability measure. The latter concepts are at the heart of the finance literature and play a unifying role in it. Moreover, by assuming that the state of the economy is well-described by factors that follow diffusion dynamics, factor-dependent expressions for prices and yields can be derived. Typically and for reasons of tractability, additional model assumptions are imposed on the factor dynamics, giving rise to the so-called affine class of term structure models. We discuss the fundamental trade-off between empirical flexibility and theoretical rigor that applies to all models within the affine class of term structure models. Recently, the class of quadratic term structure models has been proposed and seems to outperform the affine class in terms of matching the economic moments of the yield curve. However, given the lack of uniform data samples and the widely differing estimation methods, much robustness work remains to be done.
term structure of interest rates, affine term structure model, review
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