## Working Papers

### Jumps, Realized Densities, and News Premia (pdf)

Announcements and other news continuously barrage financial markets causing asset prices to jump hundreds of
times per day. Recursive utility implies that this jump-driven uncertainty will be priced differently than
equivalent diffusive-driven uncertainty. I derive a tractable nonparametric continuous-time representation for
the prices' jumps and derive the implied sufficient statistic for the jump dynamics. This statistic —
the * jump volatility * — is the instantaneous variance of the jump part and measures news risk. I
define the realized density as the daily return density conditional on its diffusion and jump volatilities.
This solves the time-aggregation problem and reduces tracking the daily return density to forecasting its
volatilities. I develop estimators for the volatilities and the realized density and estimate them using
high-frequency data from SPY. This nonparametrically identifies the average curvature in investor's certainty
equivalence functional. I then apply these methods to high-frequency data from the S&P 500 and show that total
volatility commands a positive risk premium and the proportion of volatility driven by jumps commands a
negative premium. This implies that investor's certainty equivalence function is quasiconvex. I further show
that volatility premia are capable of explaining the large ex-post return on FOMC announcement days.

### Smooth Priors and the Curse of Dimensionality:

Feasible Multivariate Density Estimation

* with Minsu Chang *

Since most economic data are multivariate, a classic problem in the literature is to estimate a multivariate density. When you have more than a couple of series, the curse-of-dimensionality makes nonparametric estimators imprecise. We provide a simple mixture representation for the conditional density of a multivariate Markov process. For any finite number of periods, the number of mixture components required to approximate the density well is a random variable. Consider an asymptotic experiment where the econometrician picks a small positive number \(\delta\), the number of series is fixed, and the number of periods \(T\) grows. We construct a bound on the number of mixture components as a function of \(T\) alone that holds with prior probability \(1-\delta\). Surprisingly, this estimator's convergence rate — \(\log(T) / \sqrt{T} \) — does not decline as the number of series. This bound exploits smoothness in the prior and does not require the likelihood to be smooth. We provide a computationally efficient Bayesian estimator using a Dirichlet process and analyze its performance in two empirical examples. The first is a monthly macroeconomic panel where our method shows consumption's conditional variance greatly increased during the Great Recession. The second is a daily financial panel where our method automatically detects the data's stylized features, including stochastic volatility and fat tails.