This article employs jump-diffusion models, including the ARJI model and the GARCH-jump model, to examine jump intensity and volatility of Taiwan stock and foreign exchange markets during a Presidential election period. The empirical results indicate that, firstly, the ARJI model fits data better than the GARCH-jump model. Secondly, the Presidential election events enhance the jump intensity of both markets and the jump-induced variance is higher than diffusion-induced variance. It reveals the importance of the discrete jump process during a Presidential election period, and might provide some implications for option pricing or hedging strategy. Due to the intervention of the Central Bank in the foreign exchange market during a Presidential election period, the results indicate that jump intensity and volatility of jump size are more moderate.