Model-based Estimation of High Frequency Jump Diffusions with Microstructure Noise and Stochastic Volatility

With the advent of high frequency data, research has been instigated into the intra-day and integrated volatility, measured through e.g. realised volatility. Such measures may be contaminated by microstructure effects and jumps, leading to the development of alternative nonparametric estimators using quadratic variation measures. Instead of using such model-agnostic, non-parametric measures, this article focuses on a high-frequency parametric model allowing explicitly for microstructure effects, jumpdiffusions, missing observations and stochastic volatility. This way a parametric measure of volatility is obtained. It allows for taking up macro-economic or other financial variables for modelling jumps in the price process, and thus help in obtaining a better understanding of the inner workings of financial markets. The performance of the model-based estimation on daily variation is compared to the non-parametric approach in both a simulation exercise and an application concerning recent S&P 500 index data. The model-based measures are found to perform better than the nonparametric methods in their fit of the integrated variation. In the application the model is found to be able to extract a measure for the spot variance jointly with an automatic detection of jumps.