Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods

We compare two approaches for estimation of stochastic volatility and jumps in the EUR//USD time series—the non-parametric power-variation approach using high-frequency returns and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We have found that the estimated jump probabilities based on these two methods are surprisingly uncorrelated (using a rank correlation coefficient). This means that the two methods do not identify jumps on the same days. We further found that the non-parametrically identified jumps are in fact almost indistinguishable from the continuous price volatility at the daily frequency because they are too small. In most cases, the parametric approach using daily data does not in fact identify real jumps (i.e. discontinuous price changes) but rather only large returns caused by continuous price volatility. So if these unusually high daily returns are to be modelled, the parametric approach should be used, but if the goal is to identify the discontinuous price changes in the price evolution, the non-parametric high-frequency-based methods should be preferred. Among other results, we further found that the non-parametrically identified jumps exhibit only weak clustering (analyzed using the Hawkes process), but relatively strong size dependency. In the case of parametrically identified jumps, no clustering was present. We further found that after the beginning of 2012, the amount of jumps in the EUR//USD series greatly increased, but the results of our study still hold.