Statistical Inference for High Frequency Data

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The project will investigate the estimation of volatility-like objects in the context of the hidden semi-martingale model. Apart from volatility, we are concerned with co-variations, ANOVA, leverage effect, and related quantities. The project uses ideas from contiguity and unbiased estimation to find such estimators. Data are assumed to have high frequency, so that small-interval asymptotics will be used. A main part of the project is concerned with the applications of such estimators. The investigator's earlier findings on nonparametric, trading based, risk management for options will be interfaced with the estimators to find complete procedures for safely unwinding dangerous positions. The estimators will also be combined with forecasting techniques to provide high-frequency based competitors to latent volatility models like GARCH. We can here draw on the martingale type error structure in the high frequency estimation. The economic value of the estimators in terms of portfolio management will also be investigated. A main background for the project is the increasing availability of high frequency data for financial securities prices. This permits, in principle, very precise determination of volatility and similar characteristics of prices. The investigator's finding, however, that prices behave as if they have measurement error, raises a number of questions about how the statistics is carried out. This project will be concerned with both estimation, and applications to risk management, forecasting, portfolio management, and regulation. The results are of interest to investors, regulators, and policymakers.