Non parametric Estimation of high-frequency Volatility and Correlation Dynamics

This thesis addresses the problem of quantitatively evaluating the temporal dynamics that characterized financial time series. In particular, we perform an accurate analysis of the Fourier estimator, a newly proposed nonparametric methodology to measure ex-post volatility and cross-volatilities as functions of time, when financial assets are observed at different highfrequency levels over the day. The estimator has the peculiar feature to employ the observed data in their original form, therefore exploiting all the available information in the sample. We first show how to considerably improve the numerical performance of the Fourier method making possible the analysis of large sets of data, as it is usually the case with high-frequency series. Secondly, we use Monte Carlo simulation methods to study the behavior of three driving parameters in the estimation procedure, when the effects of both irregular sampling and microstructure noise are taken into account. The estimator is showed to be particularly sensitive to one of these quantities, which is in turn used to control the contribution of the above effects. Integrated financial correlation is also analyzed within two distinct comparative studies that involve other multivariate measures. The analysis is then extended to consider the entire evolution of the underlying correlation process. Finally, we propose a new class of nonparametric spot volatility estimators, which is showed to include the Fourier method as a particular case. The full limit theory under infill asymptotics in the pure diffusive settings of the class is derived. Empirical evidence in support of our conclusions is also provided.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

City University London

Year dc:date.issued

2010

Author dc:creator

• Mattiussi, V.

• HB Economic Theory