Affine Term Structure Models

Abstract

The quest for understanding what moves bond yields has produced an enormous literature with its own journals and graduate courses. Those who want to join the quest are faced with considerable obstacles. The literature has evolved mostly in continuous time, where stochastic calculus reigns and partial differential equations spit fire. The knights in this literature are fighting for different goals, which makes it often difficult to comprehend why the quest is moving in certain directions. Bond yield movements over time can be captured by simple vector auto regressions in yields and maybe other macroeconomic variables. Several aspects of bond yields, however, set them apart from other variables typically used in vector auto regression studies. One aspect is that bonds are assets and that bonds with many different maturities are traded at the same time. Bonds with long maturities are risky when held over short horizons, and risk-averse investors demand compensation for bearing such risk. Arbitrage opportunities in these markets exist unless long yields are risk-adjusted expectations of average future short rates. Movements in the cross section of yields are, therefore, closely tied together. © 2010 Elsevier Inc. All rights reserved.