This article reviews the literature on sparse high-dimensional models and discusses some applications in economics and finance. Recent developments in theory, methods, and implementations in penalized least-squares and penalized likelihood methods are highlighted. These variable selection...

Using prices of both S&P 500 options and recently introduced VIX options, we study asset pricing implications of volatility risk. While pointing out the joint pricing kernel is not identified nonparametrically, we propose model-free estimates of marginal pricing kernels of the market return and...

Estimating the covariance and correlation between assets using high frequency data is challenging due to market microstructure effects and Epps effects.  In this paper we extend Xiu's univariate QML approach to the multivariate case, carrying out inference as if the observations arise from an...

We seek a closed-form series approximation of European option prices under a variety of diffusion models. The proposed convergent series are derived using the Hermite polynomial approach. Departing from the usual option pricing routine in the literature, our model assumptions have no...

Estimating the covariance and correlation between assets using high frequency data is challenging due to market microstructure effects and Epps effects. In this paper we extend Xiu’s univariate QML approach to the multivariate case, carrying out inference as if the observations arise from an...

This paper investigates the properties of the well-known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise, by extending the classic asymptotic results of quasi-maximum likelihood estimation. When trying to estimate the integrated volatility...