Modeling the Variance of Variance Through a Constant Elasticity of Variance Generalized Autoregressive Conditional Heteroskedasticity Model

This paper compares a standard GARCH model with a Constant Elasticity of Variance GARCH model across three major currency pairs and the S&P 500 index. We discuss the advantages and disadvantages of using a more sophisticated model designed to estimate the variance of variance instead of assuming it to be a linear function of the conditional variance. The current stochastic volatility and GARCH analogues rest upon this linear assumption. We are able to confirm through empirical estimation that for equity returns and for some currency crosses the variance of variance does in fact grow at a rate which exceeds the standard linear expectations.