Intraday volatility patterns from short-dated options

Abstract

We propose a nonparametric estimator for the deterministic periodic component of volatility from short-dated options within an in-fill asymptotic setting. The estimator uses options with zero and one day to expiration sampled at high-frequency during a trading day. At each point in time, we aggregate the options to form nonparametric estimates of conditional risk-neutral expectations of future integrated return variation for the two available option tenors. A suitable ratio of these estimates removes the stochastic components of the conditional expectations of future volatility, up to asymptotically higher-order terms, and allows to form estimates of the deterministic periodic component of volatility. We derive a Central Limit Theorem for the estimator, with its rate of convergence determined from the mesh of the strike grid and the length of the time to expiration of the options. The newly-developed estimation procedure is applied to S&P 500 index options data.