Realized density estimation using intraday prices

Availability of high-frequency data, in line with IT developments, enables the use of Availability of high-frequency data, in line with IT developments, enables the use of more information to estimate not only the variance (volatility), but also higher realized moments and the entire realized distribution of returns. Old-fashioned approaches use only closing prices and assume that underlying distribution is time-invariant, which makes traditional forecasting models unreliable. Moreover, time-varying realized moments support findings that returns are not identically distributed across trading days. The objective of the paper is to find an appropriate data-driven distribution of returns using high-frequency data. The kernel estimation method is applied to DAX intraday prices, which balances between the bias and the variance of the realized moments with respect to the bandwidth selection as well as the sampling frequency selection. The main finding is that the kernel bandwidth is strongly related to the sampling frequency at the slow-time-time scale when applying a two-scale estimator, while the fast-time-time scale sampling frequency is held fixed. The realized kernel density estimation enriches the literature by providing the best data-driven proxy of the true but unknown probability density function of returns, which can be used as a benchmark in comparison against ex-ante or implied driven moments.