The Option-Implied Asset Volatility Surface

Abstract

This paper provides a simple way to obtain an option-implied asset volatility surface. The proposed estimation technique allows to estimate the unobservable asset volatility surface in the same fashion of what is done when equity volatility is extracted from options. Given a sample of 66 US firms, the asset volatility is first estimated at the firm level and then aggregated in order to study the properties of the market-wide asset volatility surface. Principal component analysis (PCA) is conducted on the weekly changes of the volatility surface both across the moneyness and the time-to-maturity dimension, as well as on the overall surface. Both across moneyness and maturity, the first three PCs are able to account for most of the variation and can be identified as level, slope/smirk and curvature factors respectively. When analysed in across the whole surface, the first two PCs account for most of the variation and represent a level and a skew factor. Finally, the joint evolution of the smirk and the slope of the surface is model-led as a Vector Auto-regressive model with exogenous variables. Both slope and smirk appear to be jointly auto-correlated and loading of the other market variables display the predicted sign.