Functional PCA for Implied Volatility Surface Prediction

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Functional PCA for Implied Volatility Surface Prediction

May. 19, 2020

The volatility surface of an option changes over time, and values exist as discrete points on a grid, but the property of smoothness across points on the surface is evident. Common approaches to predicting points on an implied volatility surface include generalized autoregressive conditional heteroskedasticity (GARCH) and Vector Autoregression (VAR) models. These models involve modelling each point on the grid at a time and thus don’t incorporate the smoothness typical to a volatility surface. To incorporate this effect, we propose to use a combination of functional data analysis and nonlinear regression modelling for predicting implied volatility while respecting the functional nature of the surface.

  • Implied Volatility surfaces can be represented in significantly lower dimensions with little loss of information. 
  • The projection of implied surfaces to lower dimensions via functional principal component analysis (FPCA) respects the geometric nature of the surfaces while maintaining a minimal loss of information.
  • The projection of implied volatility surfaces to lower dimensions via FPCA provides a framework for forecasting values of implied volatility by forecasting values of principal component scores.
  • There is evidence of the predictability of the principal component scores of implied volatility surfaces.
  • Using a standard forecasting method (VAR) for forecasting implied volatility results in lower out-of-sample error when using principal component scores as features when compared to the same method using all points on the surface.