Implied volatility surfaces during the period of global financial crisis

This paper adopts a parametric regression approach to model and calibrate implied volatility surface during the period of the global financial crisis. Due to its relatively low computational cost, it facilitates comparison across a great number of different competing models. The proposed regression models are backtested against historical S&P 500 prices during both volatile and non-volatile periods as proxied by the VIX index around the same time period, and the fits of the models are assessed. Furthermore both an equally weighted scheme and an alternative scheme based on observed implied volatilities as the weight are deployed and the results produced by these two schemes are contrasted and compared. Finally the concept of promptness, instead of the more traditional concept of time to maturity, is introduced as a covariate in the regression models to better capture the shape of the volatility surface during the period characterized by a prolonged low interest-rate environment.