How Far Apart Can Two Riskless Interest Rates Be?(One Moves, the Other One Does Not)

In the presence of transactions costs, no matter how small, ar-bitrage activity does not necessarily render equal all riskless rates ofreturn. When two such rates follow stochastic processes, it is not opti-mal immediately to arbitrage out any discrepancy that arises betweenthem. The reason is that immediate arbitrage would induce a de…niteexpenditure of transactions costs whereas, without arbitrage interven-tion, there exists some, perhaps su¢ cient, probability that these twointerest rates will come back together without any costs having beenincurred.[...]