Modeling Variance of Variance: The Square-Root the Affine and the CEV GARCH Models (original) (raw)

This paper,develops,a new,econometric,framework,for investigating,how,the sensitivity of the financial market volatility to shocks varies with the volatility level. For this purpose, the paper first introduces,the square-root (SQ) GARCH model,for financial time series. It is an ARCH analogue,of the continuous-time,square-root stochastic volatility model,popularly,used in derivatives pricing and hedging.,The variance,of variance,is a linear function of the conditional,variance,in the SQGARCH and of the square of it in the GARCH. After showing some implications of this difference, the paper introduces the constant-elasticity-of-variance (CEV) GARCH model, which allows more flexible fitting of variance-of-variance dynamics. The paper develops conditions for stationarity, the existence of finite moments, β-mixing, and other properties of the conditional variance process via the general state-space Markov chains approach. In particular, the paper generalizes the strict stationarity condi...