Essays on Realized Covariance Estimation
Scientific disciplinary sector
Corso di studi
SCIENZE ECONOMICHE E MANAGERIALI - International Doctoral Program in Economics
relatore BOTTAZZI, GIULIO
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Data inizio appello
The present dissertation develops methods of the estimation of the whole day covariance matrices based on available intraday high-frequency data. <br>In the first chapter, existing literature is reviewed. In empirically-oriented literature, it is argued that overnight returns appear to follow different price processes than returns within the trading day. In particular, overnight returns have lower volatility, higher Sharp ratios, higher tail risk, and higher correlations. Moreover, according to some studies, intraday and overnight volatilities mutually influence each other. Methodological literature proposes a number of models for univariate overnight realized volatility estimations, as well as correction procedures for covariance estimation in asynchronous markets based on daily data. Given the variety of existing approaches, it should be stated that there is an absence of high-frequency based methods for a whole day covariance estimation (except for very naive and noisy methods), both for synchronous and asynchronous case. <br>Chapter 2 and 3 of the present work fill this gap. In the second chapter a new concept of linear algebra is defined: proportionality of positive semidefinite symmetric matrices. It is based on existing concept of geometric means of the matrices. Direct proportionality function Y(X) is defined as: Y(X) = SXS; where S is some positive semi-definite symmetric matrix, called ’scaling’ matrix. <br>The second chapter deals with the problem of estimation of the whole day covariance, based on intraday realized covariance matrix and a vector of overnight return. Assuming that overnight covariance is ’proportional’ to the intraday covariance, two conditionally unbiased estimators are obtained: one based only on intraday realized covariance, and the other one based only on overnight returns. They are weighted in a way, allowing to decrease the noise of the resulting estimator. <br>The third chapter is devoted to covariance in asynchronous markets. In this case, volatilities are estimated using regular methods, while the whole day correlation is assumed to be a function of realized correlation during overlapping period. A whole day correlation is obtained from ’rescaled’ covariance of overlapping period. A time series of whole day covariance matrices was used as input to the forecasting models. A bivariate extension of HAR model was proposed and compared with other multivariate HAR specification and EWMA model. Both estimators as well as forecasting model were tested on real high-frequency data, and show a higher degree of precision then existing approaches.