Simplicity vs. Complexity: Jump Diffusions in Affine Term Structure Models

Affine Jump Term Structure Models (AJTSMs) add a jump diffusion component to Affine Term Structure Models (ATSMs) to model the term structure of interest rates. I investigate whether there is a significant difference in the in- and out-of-sample performance of ATSMs and AJTSMs for riskless interest rates in pre-, mid- and post-crisis periods. I consider the one-, two- and three-factor Vasicek model within the ATSM-and AJTSM-framework and use Quasi-Maximum Likelihood Estimation (QMLE) to estimate the parameters. Firstly, I find that the three-factor AJTSM is unidentified and that imposed restrictions result in an unrealistic economic model. Secondly, the results show that jump diffusion components are empirically justified in the complete sample and pre- and mid-crisis samples. Thirdly, goodness-of-fit measures show that the in-sample fit of one- and two-factor ATSMs and AJTSMs is poor. The three-factor ATSM is superior in fitting the yield curve of the riskless interest rates. Lastly, I establish that ATSMs and AJTSMs perform poorly in out-of-sample VaR and ES estimation for Risk Management purposes.