Principal-Component-Based Gaussian Affine Term Structure Models: Constraints and Their Financial Implications

International Journal of Theoretical and Applied Finance, Vol. 23 N° 2 pp. 1 - 36, March 2020

This work builds on the work by Joslin et al. [(2011) A new perspective on Gaussian dynamic term structure Models, The Review of Financial Studies 24, 926–970] on the affine dynamics of portfolios of yields and addresses the unresolved issues of ‘internal consistency’ mentioned in the same paper. It shows the unexpected constraints that have to be satisfied by the ℚ-measure evolution of the yield curve if the portfolio of yields has to be interpreted as their principal components. This choice of state variables is common in the recent literature and so our findings are intrinsically interesting. However, we show that our results also extend to a wide class of choices for state variables, when these are chosen as linear combinations of yields. We show that these constraints have important financial consequences, which, to our knowledge, have not been appreciated. In particular, this paper highlights some puzzling issues of compatibility between the ℚ- and ℙ-measure dynamics of Gaussian dynamic term structure models when principal components are chosen as state variables, once the constraints we derive are taken into account.

Keywords: Affine term structure models, principal components, risk premia, market price of risk