VOLATILITY ESTIMATION IN MISSING AT RANDOM HIGH-FREQUENCY FINANCIAL TIME SERIES

Abstract

More than 15 years ago, the capital markets have seen significant development, introducing high-frequency trading and a shift of market towards high-frequency and algorithm trading. It was always believed that high-frequency trading and automated trading were source price shocks and rising of volatility. Therefore, more interest was recently given in modeling the volatility with high-frequency financial data. However, financial data can still be missing despite modern technology that allows data collection on a very fine time scale. Thus, this thesis focuses on the estimation of regression and volatility functions based on missing data using a nonparametric heteroscedastic regression model. A Nadaraya-Watson type estimator is used when the response variable is a real-valued random variable and subject to missing at random mechanism, while the predictor is a completely observed infinite-dimensional (functional) random variable. Based on the observed data, we first introduce a simplified, as well as inverse probability weighted, estimators. Second, these initial estimators are used to impute missing values and define estimators of the regression and volatility operators based on imputed data. Third, the performance of the proposed estimators is assessed using simulated data. Finally, an application to the estimation and forecasting of the daily volatility of Brent Oil Price returns conditionally to 1-minute frequency daily Natural Gas returns curves is also investigated.