One of the issues of risk management is the prediction of credit risk and financial risk. This paper investigates the tail constancy of extreme behavior of changes of TED Spread rate and changes of LIBOR-OIS Spread rate. Due to recent fluctuations in global financial markets that cause the TED Spread rate and LIBOR-OIS Spread surging to the historical record, this paper investigate whether the extreme change in the change of rate are predictable based on the past extremities. These answers are important issues as the change of TED spread rate and change of LIBOR-OIS Spread rate are taken advantage of considering and predicting markets toward future global economic condition in general, and credit risks in particular. In the current paper, we firstly employ EVT to examine the tail behavior of the distribution of the changes of TED Spread rate, and changes of LIBOR-OIS Spread rate by Hill estimator (Hill, 1975), for tail index estimation. Next, we apply breakpoint test proposed by Quintos et al. (2001) to detect the structural change in tail index in distribution of changes of rate. Finally, we estimate VaRs for the next trading date for TED Spread and LIBOR-OIS under various probabilities of occurrences.