Nonparametric Filtering of Conditional State-Price Densities

This paper studies the use of noisy high-frequency data to estimate the time-varying state-price density implicit in European option prices. A dynamic kernel estimator of the conditional pricing function and its derivatives is proposed that can be used for model-free risk measurement. Infi ll asymptotic theory is derived that applies when the pricing function is either smoothly varying or driven by diffusive state variables. Trading times and moneyness levels are modelled by marked point processes that capture intraday trading patterns. A simulation study investigates the performance of the estimator using a varying plug-in bandwidth in various scenarios. Empirical analysis using S&P 500 E-mini European option quotes reveals signi ficant time-variation at intraday frequencies. An application towards delta- and minimum variance-hedging further illustrates the use of the estimator