Online Prediction of the Volatility of High-Frequency Financial data

Specialeforsvar ved Nicklas Haseriis Werge

Titel: Online Prediction of the Volatility of  High-Frequency Financial Data

Abstract: The aim of the thesis is to understand and predict highly volatile financial data, such as log-returns, in a high-frequency setting. We will analyze an appropriate recursive procedure for the volatilities of the Generalized Auto Regressive Conditional Heteroscedastic (GARCH) model, and to present a stability condition of the online Quasi Minimum Likelihood Estimator (QMLE). The key problem of the statistical analysis of the GARCH model is prediction of volatilities. In this thesis we construct a recursive online algorithm for prediction of the volatilities in a GARCH process in real time. Our focus for this very rapidly flow of observations, is adaptive online procedures. The proposed algorithm construction and their convergence properties are based on the theory of stochastic approximation from [Robbins & Monro 1951] namely the Stochastic Gradient Descent (SGD). In order to estimate the GARCH parameters in the framework of the SGD theory we need to treat the problem of stability of the algorithms. For the applicability of the SGD theory we have developed two useful technical tools: a simple method for ensuring stability of the computation recursive algorithm and under some specific assumptions we have convexity in the GARCH model. The performance of the online algorithms is demonstrated by experimental result both for simulated and real high-frequency financial data. 

Vejleder: Olivier Wintenberger
Censor:   Christoffer Kanstrup, Danske Bank