Publications
Semiparametric Estimation of Latent Variable Asset Pricing Models
Journal of Econometrics (2023), Volume 236, Issue 1
Matlab code
This paper studies semiparametric identification and estimation of consumption-based asset pricing models with latent state variables. We model consumption, dividends, and prices via unknown functions of Markovian state variables describing aggregate output growth. Subsequently, we identify state-dependent components in stochastic discount factor models based on the Euler equation. We develop tractable algorithms for filtering, smoothing, and sieve maximum likelihood estimation, and establish its consistency. Empirically, we find sizable nonlinearities in the impacts of expected growth and volatility on the price-dividend ratio and the discount factor.
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
Estimating a Conditional Density Ratio Model for Asset Returns and Option Demand (July 2025), with Oliver Linton. Conditionally accepted, Journal of Econometrics
Option-implied risk-neutral densities are widely used for constructing forward-looking risk measures. Meanwhile, investor risk aversion introduces a multiplicative pricing kernel between the risk-neutral and true conditional densities of the underlying asset’s return. This paper proposes a simple local estimator of the pricing kernel based on inverse density weighting. We characterize the asymptotic bias and variance of the estimator and its multiplicatively corrected density forecasts. The estimator with plug-in bandwidths performs well in a simulation study. A local exponential linear variant is proposed to include conditioning variables. We apply our estimator to a demand-based model for S&P 500 index options using net positions data, and attribute U-shaped pricing kernels to heterogeneous beliefs about volatility.
Semiparametric Estimation of Probability Weighting Functions Implicit in Option Prices (March 2025), with H. Peter Boswijk, Roger J.A. Laeven, and Niels Marijnen
This paper develops a semiparametric estimation method that separately identifies the probability weighting and utility functions implicit in option prices. Our profile maximum likelihood estimator avoids directly specifying the conditional return distributions, and instead relies on kernel smoothing of suitable probability integral transforms. We establish the asymptotic properties of the estimator, and report its good finite sample performance in Monte Carlo simulations. Empirical results based on S&P 500 index option prices and returns over the period 1996–2023 reveal pronounced inverse S-shapes in the probability weighting functions, that are robust to various specifications of the utility function of wealth.
Efficient Estimation of Pricing Kernels and Market-Implied Densities (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
“Learning about Macroeconomic and Financial Tail Risks”, with Jasmine Xiao
“Recovering Risk and Risk Aversion in a Nonlinear Asset Pricing Model”