This article explores the time-series behavior of correlations of returns, volatilities of returns, volatilities of volatilities, and correlations of volatilities in domestic and international financial markets such as equity (indices), interest rates (bonds), and currency (exchange rates) using a Kalman filter approach to estimate the aforementioned parameters. The main findings include the following. First, the correlations of risk factors are highly unstable over time, both in terms of sign and absolute value. Second, the time variation of risk-factor volatilities is stochastically nonlinear. Long periods of deterministic volatilities are interrupted by sudden bursts of highly volatile periods. Third, daily volatilities of risk-factor volatilities fluctuate over time within a narrower band. Fourth, the correlations between volatilities are generally positive and relatively stable over time. These results have implications for financial risk management, dynamic asset allocation, and valuation of derivative securities. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:1119–1146, 2002