This paper studies the correlation and volatilities of the bond and stock markets in a regime- switching bivariate GARCH model. We extend the univariate Markov-Switching GARCH of Haas, Mittnik and Paolella (2004) into a bivariate Markov-switching GARCH model with Conditional Constant Correlation (CCC) speciÖcation within each regime, though the correlation may change across regimes. Our model allows separate state variable governing each of the three processes: bond volatility, stock volatility and bond-stock correlation. We Önd that a separate state variable for the correlation is needed while the two volatility processes could largely share a common state variable, especially for the 10-year bond paired with S&P500. The "low-to-high" switching in stock volatility is more likely to be associated with the "high-to-low" switching in correlation while the "low-to-high" switching in bond volatility is likely to be associated with the "low-to-high" switching in correlation. The bond-stock correlation is signiÖcantly lower when the stock market volatility is in the high regime, but higher when the bond volatility is in its high regime.
