The Nelson-Siegel Model of the Term Structure of Option Implied Volatility and Volatility Components

We develop the Nelson-Siegel model in the context of option-implied volatility term structure and study the time-series of three volatility components in the model. We show that these components, corresponding to the level, slope and curvature of the volatility term structure, can be interpreted as the long-, medium- and short-term volatilities. The long-term component is persistent, and the short-term component is highly correlated with the VIX index. We further demonstrate that macroeconomic and financial variables help explain these volatility components. The long-term component is driven by macroeconomic variables, the medium-term by market default risk and the short-term by financial market conditions. These are revealing because after decades of research existing literature have failed to link these variables to option pricing. We also show that the Nelson-Siegel model has superior performance in forecasting the volatility term structure, compared with the popular implied volatility function method and the Heston stochastic volatility model. Finally, we demonstrate that the three-factor Nelson-Siegel model is better in out-of-sample prediction than a two-factor model, providing support to the literature of component volatility models.