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Analysis of Asymmetric GARCH Volatility Models with Applications to Margin Measurement

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We explore properties of asymmetric generalized autoregressive conditional heteroscedasticity (GARCH) models in the threshold GARCH (GTARCH) 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 lowfrequency volatility component. We then apply a variety of volatility models in setting
initial margin requirements for a central clearing counterparty (CCP). Finally, we show how to mitigate procyclicality of initial margins using a three-regime threshold autoregressive model.