Term Structure Models with Parallel and Proportional Shifts

The paper investigates the possibility of an arbitrage-free model for the term structure of interest rates where the yield curve only changes through a parallel shift. HJM type forward rate models driven by a multidimensional Wiener process and by a general marked point process are considered. Within this general framework it is shown that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. It is also shown that there exists no nontrivial flat term structure model. The same analysis is repeated for a similar case, in which the yield curve only changes through proportional shifts.