GARCH option pricing and implied FX volatility indices

Abstract

Abstract The focus of this paper is the foreign exchange (FX) variance risk premium and the modelling of FX volatility indices of both a developed (United States Dollar) and an emerging market (South African Rand). Regarding the methodology, the variance risk premium is estimated as the difference between realised variance and the variance obtained from the volatility index, and different univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH) models are considered for the modelling of the volatility index. Empirical results indicate that the variance risk premium is negative on average, this is consistent with previous findings in the literature. Furthermore, asymmetric GARCH models outperform the symmetric GARCH model when modelling FX implied volatility indices.