# Returns, volatility and durations of high frequency financial data

Yan, Xiufeng (2021) Returns, volatility and durations of high frequency financial data. Doctoral thesis (PhD), University of Sussex. PDF - Published Version Download (3MB)

## Abstract

This dissertation consists of three chapters investigating the modelling of financial tick-by-tick data. Financial research using high-frequency data have been very active during the last two decades. The financial mathematical modelling of the high frequency price dynamics is based on the proper interpretation of the characteristics of the tick-by-tick data.

The first chapter provides an empirical investigation of the tick-by-tick returns. First, I provide a sampling method of returns different from the sampling from identical time interval. Second, I compare the returns from the two sampling methods using the Central Limit Theorem. The empirical results suggest that sampling returns from identical number of tick-by-tick transactions could recover the normality of intraday returns at lower costs due to its faster convergent rate.

The second chapter proposes a multiplicative component intraday volatility model. The intraday conditional volatility is expressed as the product of intraday periodic component, intraday stochastic volatility component and daily conditional volatility component. I extend the multiplicative component intraday volatility model of Engle (2012) and Andersen and Bollerslev (1998) by incorporating the durations between consecutive transactions. The model can be applied to both regularly and irregularly spaced returns. I also provide a nonparametric estimation technique of the intraday volatility periodicity. The empirical results suggest the model can successfully capture the interdependency of intraday returns.

The third chapter explores the duration dynamics modelling under the Autoregressive Conditional Durations (ACD) framework (Engle and Russell 1998). I test different distributions assumptions for the durations. The empirical results suggest unconditional durations approach the Gamma distributions. Moreover, compared with exponential distributions and Weibull distributions, the ACD model with Gamma distributed innovations provide the best fit of SPY durations.

Key Words: tick-by-tick data, Intraday volatility, Intraday seasonality, marked point process, UHF-GARCH models, intraday returns, Autoregressive Conditional Duration models, realized volatilities.

Item Type: Thesis (Doctoral) School of Mathematical and Physical Sciences > Mathematics H Social Sciences > HG Finance > HG0101 Theory. Method. Relation to other subjects > HG0106 Mathematical models Library Cataloguing 12 Apr 2021 09:52 12 Apr 2021 09:52 http://sro.sussex.ac.uk/id/eprint/98403

View download statistics for this item