Modeling And Statistical Inference For High-frequency And/or Low-frequency Financial Data

In financial markets,modeling and forecasting play a central role in risk management,option pricing,and investment portfolios.The early research on volatility is mainly based on lowfrequency financial data,such as daily,weekly,monthly,quarterly or annual data,which may contain less information about asset prices.Due to the advantages that high-frequency data is easily accessible and contains a wealth of information,literature related to the financial market volatility based on intraday data has exploded in recent years.However,the discretetime models for low-frequency data and continuous-time models for high-frequency data have developed quite independently and there seems to be a lack of study of another fundamental quantity,i.e.,volatility of volatility,for high-frequency data.This paper aims to analyze and study the volatility of high-frequency data and/or low-frequency data in different market environments,including volatility analysis for the GARCH-It?-Jumps model based on the highfrequency and low-frequency financial data,statistical inference for GQARCH-It?-Jumps model based on the realized range volatility,and the estimation of integrated volatility of volatility by the range-based volatility measure.The main contents are constructed as follows:Chapter 1 is to introduce the background,recent methods,and some problems to be solved for high-frequency data and low-frequency data,as well as the main contents and creativity of my studies.Chapter 2 develops a model that can accommodate both the continuous-time-diffusion and the discrete-time Mixed-LARCH-Jump models by embedding the discrete Mixed-GARCHJump structure in the continuous volatility process,which considers the impacts of price jumps and volatility jumps on volatility.A Griddy-Gibbs sampler approach is proposed to estimate parameters.The volatility forecasting and Value at Risk(VaR)forecasting based on the Peaks Over Threshold(POT)are developed.In addition,a set of simulations are carried out to check the finite sample performance of the proposed methodology.Specially,empirical studies show that in general volatility is influenced more seriously by continuous innovations than extreme reactions.Chapter 3 proposes a generalized model termed as "GQARCH-It?-Jumps model",which not only accounts for the continuous dynamic asymmetric effect of the price on volatility but also considers co-jumps in the price and volatility processes.The quasi-likelihood functions for the low-frequency GQARCH structure are developed for the parametric estimations.In the likelihood functions,for high-frequency financial data,the realized range-based volatility estimators are adopted as the "observations",rather than the realized return-based volatility estimators which entail the loss of intra-day information of the price movements.The asymptotic theories are mainly established for the proposed estimators.Moreover,simulation studies are implemented to check the finite sample performance of the proposed methodology and empirical data exemplifies the performance of the proposed method.Chapter 4 provides new statistics to estimate the integrated volatility of volatility by the range-based volatility measure in the presence of microstructure noise and/or price jumps.The associated unfeasible and feasible center limit theorems with convergence rate n-1/8 for the new estimators are established in the presence of microstructure noise and/or price jumps.Finally,simulation studies are conducted to check the finite sample performance of the proposed methodology and a real study is discussed later.