LONG FORWARD AND ZERO-COUPON RATES CAN NEVER FALL

In frictionless markets having no arbitrage, the asymptotic zero-coupo n rate never falls. The same is true of the long forward rate. The lon g par-coupon rate can rise and fall due to forward rate movements at s hort maturities. This article relates the three types of interest rate and formalizes and proves the impossibility results for falling asymp totic rates. These results can be tested in a parametric term structur e specification that is rich enough to identify a time series of long rates. The results show that it is not possible to specify arbitrarily the long forward or zero-coupon rate process.