Empirical studies have shown that a large number of financial asset returns exhibit fat tails (leptokurtosis) and are often characterized by volatility clustering and asymmetry. This paper considers the ability of the asymmetric GARCH-type models (TGARCH, EGARCH, APGARCH) to capture the stylized features of volatility in the Chicago Board Options Exchange Volatility Index (VIX). We analyzed daily VIX returns for the period September 26th, 2012 - September 27th, 2017. The results of this paper suggest that in the presence of asymmetric responses to innovations in the market, the EGARCH (1,1) Student-t model which accommodates the kurtosis of VIX return series is preferred.