Park, Sujin
(2011)
Consistent estimator of ex-post covariation of discretely observed diffusion processes and its application to high frequency financial time series.
PhD thesis, London School of Economics and Political Science.
Abstract
First chapter of my thesis reviews recent developments in the theory and practice of
volatility measurement. We review the basic theoretical framework and describe the
main approaches to volatility measurement in continuous time. In this literature the
central parameter of interest is the integrated variance and its multivariate counterpart. We describe the measurement of these parameters under ideal circumstances
and when the data are subject to measurement error, microstructure issues. We also
describe some common applications of this literature.
In the second chapter, we propose a new estimator of multivariate ex-post volatility that is robust to microstructure noise and asynchronous data timing. The method
is based on Fourier domain techniques. The advantage of this method is that it does
not require an explicit time alignment, unlike existing methods in the literature. We
derive the large sample properties of our estimator under general assumptions allowing for the number of sample points for different assets to be of different order of
magnitude. We show in extensive simulations that our method outperforms the time
domain estimator especially when two assets are traded very asynchronously and with
different liquidity.
In the third chapter, we propose to model high frequency price series by a timedeformed L´evy process. The deformation function is modeled by a piecewise linear
function of a physical time with a slope depending on the marks associated with
intra-day transaction data. The performance of a quasi-MLE and an estimator based
on a permutation-like statistic is examined in extensive simulations. We also consider
estimating the deformation function nonparametrically by pulling together many time
series. We show that financial returns spaced by equal elapse of estimated deformed time are homogenous. We propose an order execution strategy using the fitted deformation time
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