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.
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.
Work in Progress
Recent evidence suggests that the market risk premium is highly volatile. I propose a model-free approach to measure how much of this variation can be attributed to changing beliefs versus changing risk preferences. The approach is based on a variance decomposition of forward-looking risk-neutral densities and the conditional pricing kernel for each value of the market return. This is implemented by a nonparametric empirical likelihood procedure which efficiently incorporates the no-arbitrage conditions into the conditional density estimator. Empirical results using S&P 500 index options point towards substantial return predictability at short horizons, and provide new insights on the ability of investors to predict tail events.
The Demand For Risk Sharing in OTC Derivative Markets (with Oliver Linton)