Analysis of Asymmetric GARCH Volatility Models with Applications to Margin Measurement

We explore properties of asymmetric generalized autoregressive conditional heteroscedasticity (GARCH) models in the threshold GARCH family and propose a more general Spline-GTARCH model, which captures high-frequency return volatility, low-frequency macroeconomic volatility as well as an asymmetric response to past negative news in both autoregressive conditional heteroscedasticity (ARCH) and GARCH terms. Based on maximum likelihood estimation of S\&P 500 returns, S\&P/TSX returns and Monte Carlo numerical example, we find that the proposed more general asymmetric volatility model has better fit, higher persistence of negative news, higher degree of risk aversion and significant effects of macroeconomic variables on the low frequency volatility component. We then apply a variety of volatility models including asymmetric GARCH, GARCH and EWMA in setting initial margin requirements for central clearing counterparties (CCPs)