We propose a general GARCH framework that allows the predict volatility using returns sampled at a higher frequency than the prediction horizon. We call the class of models High FrequencY Data-Based PRojectIon-Driven GARCH, or HYBRID-GARCH models, as the volatility dynamics are driven by what we...

In this paper, we develop a new nonparametric approach for estimating the risk-neutral density of asset price and reformulate its estimation into a double-constrained optimization problem. We implement our approach in R and evaluate it using the S&P 500 market option prices from 1996 to 2015. A...