Functional Data Analysis for Volatility

Abstract

We introduce a functional volatility process for modeling volatility trajectories for high frequency observations in financial markets. The observed volatility of returns results from this underlying process in combination with a multiplicative white noise. The proposed representation enables us to invoke functional data methodology. We describe the model and implementation and provide asymptotic justifications and consistency results in the limit as the frequency of observed trades increases. The approach is illustrated with an analysis of intra-day volatility patterns of the S&P 500 index. As we demonstrate, the proposed model not only leads to the identification of persistent reoccurring patterns, but also to successful prediction of future volatility, through the application of functional regression and prediction techniques.

Keywords: Difusion model, Functional Principal Component, Functional Regression, Market Returns, Noise contamination, Prediction, Volatility Process, Trajectories of Volatility

JEL Classification: C14, C51, C52, G12, G17