This article estimates regime-switching continuous-time stochastic volatility models using daily KOSPI 200. We consider single regime Heston, GARCH, and CEV stochastic volatility models and 6 regime-switching stochastic volatility models which have two different regimes $L$ and $H$. We employ Hamilton algorithm (Hamilton (1989)) to compute the log-likelihood and to apply MLE. Because the true transition probability density functions (TPDFs) of our stochastic volatility models are unknown, we use Ait-Sahalia (2008) and Choi (2015b) to obtain closed-form approximate TPDF. The regime-switching CEV model where the transition probability is allowed to vary over time has been found to be the best to explain the movements of KOSPI 200. Regime $L$ has a stronger leverage effect than regime $H$. Comparing to regime $L$, the volatility variable tends to revert to its long-run mean level more rapidly, the volatility of volatility variable is greater, the probability of staying in the same regime $H$ in the next period is bigger in regime $H$. And the transition probability varies with time depending on the stock price rather than the volatility. When the probabilities of regime $H$ are high we could identify various economic and political events between South Korea and North Korea or inside or outside South Korea that could have affected Korean stock market.