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Nonparametric Filtering of Conditional State-Price Densities

This paper studies the use of irregularly spaced high frequency data to estimate the state-price density (SPD) implicit in option prices. Their large sample size allows estimation of the conditional SPD at any time point of interest, which can be directly used for model-free pricing, hedging and conditional risk measurement. We develop asymptotic theory for a time-varying kernel estimator when the trading times are modelled by point processes whose intensity goes to infinity. The pricing errors and strike prices are mixing, locally stationary time series, which can be weakly dependent with the trading times. Unlike realized volatility estimation, the market microstructural noise in recorded option prices is averaged out and there is no need to subsample the data. We apply the estimator to S&P 500 E-mini European call and put option mid quotes using an iterated plug-in bandwidth, and document the intraday dynamics of the SPD and derived quantities.