THE PURPOSE OF THIS CHAPTER

In the approach taken in this book, we model the yield curve by decomposing its shape into an expectations term, a term-premia component and a convexity contribution. This decomposition is universally, if not always explicitly, accepted in the literature. However, far less attention has been devoted to the study of the third contributor (convexity) than to the other two – or, for that matter, than to liquidity (see, eg, Fontaine and Garcia (2012)) or even to the effect of the zero bound (see, eg, Wu and Xia (2014)). An early classic paper by Brown and Schaefer (2000) discussed the qualitative effect of convexity on the long end of the yield curve and provided some semi-quantitative estimates of the magnitude of the effect. However, we are not aware of a quantitative study of whether convexity is ‘fairly’ priced in themost liquid government bond market, ie, Treasuries. This is surprising, because the ‘value of convexity’ (ie, the difference between the market yields and the yields that would prevail in the absence of convexity) is substantial, as Figure 22.1 clearly shows. In this chapter we try to fill this empirical gap.

Of course, speaking of fairness makes reference to a modelling approach, and, probably herein lies the problem: in studies of this type, one always tests a joint hypothesis, that the convexity is correctly priced and the model correctly specified. Given the great uncertainty in model specification, any possible rejection must therefore always include a caveat with particularly lurid health warnings.

It is for this reason that we adopt in the analysis that follows the quasimodel- agnostic approach described in Chapter 21. By this we mean that we do place ourselves in an affine-modelling framework, but we make our results as independent as possible from the specifics of any affine model (such as the number of factors, or the nature of the state variables – latent, specified, yield curve–based, macroeconomic, etc). We only require that some affine model should exist, capable of recovering the market yield curve and yield covariance matrix with the precision required by our study.