Contrary to popular belief, the diffusion limit of a GARCH variance process is not a diffusion model unless one makes a … very specific assumption that cannot be generalized. In fact, the normal GARCH(1,1) prices of European call and puts are … identical to the Black-Scholes prices based on the average of a deterministic variance process. In the case of GARCH models with …

GARCH processes constitute the major area of time series variance analysis hence the limit of these processes is of … considerable interest for continuous time volatility modelling. The limit of the GARCH(1,1) model is fundamental for limits of … other GARCH processes yet it has been the subject of much debate. The seminal work of Nelson (1990) derived this limit as a …

ability of fifteen different GARCH models to capture the characteristics of historical daily returns effectively and generate … realistic implied volatility skews. Using many different model selection criteria we conclude that a normal mixture GARCH model … regimes (‘normal’ and ‘crash’). We also find that asymmetric normal mixture GARCH models, even without a volatility risk …

affine and non-affine specifications, possibly augmented with jumps. Jumps in one-factor models occur frequently, but add … that sudden jumps in the VIX are more likely during tranquil periods and the days when jumps occur coincide with major …

affine and non-affine specifications, possibly augmented with jumps. Jumps in one-factor models occur frequently, but add … that sudden jumps in the VIX are more likely during tranquil periods and the days when jumps occur coincide with major …

In this paper, we present an alternative to the Black Scholes model for a discrete time economy using GARCH-type models …

determined for four major currencies using an iterated cumulative sums of squares (ICSS)-GARCH model. Employing a standard GARCH … reduces volatility persistence and the significance of the ARCH and GARCH coefficients. In terms of hedging effectiveness, the … ICSS-GARCH model outperforms the standard GARCH model for all four currencies. In comparison to two constant volatility …