We apply a variety of volatility models in setting the initial margin requirements for central clearing counterparties (CCPs) and show how to mitigate procyclicality using a three-regime threshold autoregressive model. In order to evaluate the initial margin models, we introduce a loss function with two competing objectives: risk sensitivity and procyclicality mitigation. The trade-off parameter between these objectives can be selected by the regulator or CCP, depending on the specific preferences. We also explore the properties of asymmetric generalized autoregressive conditional heteroscedasticity (asymmetric GARCH) models in the threshold GARCH family, including the spline-generalized threshold GARCH model, which captures high-frequency return volatility and low-frequency macroeconomic volatility as well as an asymmetric response to past negative news in both past innovations (ARCH) and volatility (GARCH) terms. We find that the more general asymmetric volatility model has a better fit, greater persistence of negative news, a higher degree of risk aversion and an important effect on macroeconomic variables for the low-frequency volatility component of the Standard & Poor’s 500 and S&P/Toronto Stock Exchange returns.