#### Publications

**Nonparametric Filtering of Conditional State-Price Densities***Journal of Econometrics* (2020), 214(2):295-325

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. Infill 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 modeled 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 significant time-variation at intraday frequencies. An application towards delta- and minimum variance-hedging further illustrates the use of the estimator.

#### Working Papers

**Semiparametric Estimation of Latent Variable Asset Pricing Models**

– This version: April 2020

This paper studies semiparametric identification and estimation of the stochastic discount factor in consumption-based asset pricing models with latent state variables. The measurement equations for consumption and dividend shares are specified nonparametrically to allow for robust updating of the Markovian states describing the aggregate growth distribution. For the special case of affine state dynamics and polynomial approximation of the measurement equations, we derive rank conditions for identification, tractable filtering algorithms for likelihood estimation, and closed-form expressions for risk premia and return volatility. Empirically, we find sizable nonlinearities and interactions in the impact of shocks to expected growth and volatility on the consumption share and the discount factor, that help explain the divergence between macroeconomic and stock market volatility.

**Efficient Estimation of Pricing Kernels and Market-Implied Densities**

– This version: May 2021

This paper studies the nonparametric identification and estimation of projected pricing

kernels implicit in European option prices and underlying asset returns using conditional

moment restrictions. The proposed series estimator avoids computing ratios of estimated

risk-neutral and physical densities. Instead, we consider efficient estimation based on the

conditional Euclidean empirical likelihood or continuously-updated GMM criterion, which

takes into account the informativeness of option prices of varying strike prices beyond observed

conditioning variables. In a second step, we convert the implied probabilities into predictive

densities by matching the informative part of cross-sections of option prices. Empirically,

pricing kernels tend to be U-shaped in the S&P 500 index return given high levels of the

VIX, and call and ATM options are more informative about their payoff than put and OTM

options.

#### Work in Progress

** The Demand For Risk Sharing in OTC Derivative Markets** (with Oliver Linton)