Type
Text
Type
Dissertation
Advisor
Mullhaupt, Andrew Peter | Rachev, Svetlozar | Xing, Haipeng | Smith, Noah.
Date
2013-12-01
Keywords
Applied mathematics | cross-sectional volatility, EH model, EM algorithm, factor model, Jeffrey's Prior, spike phenomenon
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/77588
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
In this thesis we study the problem of modeling cross-sectional volatility structure of U.S. stock market. The thesis contains two parts. In the first part we identify a particular volatility spike phenomenon, that the cross-sectional volatility is significantly stronger at every 5 minute. An empirical spike study is conducted on individual stock level by applying Lee-Mykland jump detector. By constructing spike ratio statistics, the evolving paths of this spike phenomenon is studied during the 1993 to 2009 time period. In the second part, we model the volatility structure using factor structures. Particular, we propose two approaches to build a better model for small sample size problem, which is a common issue for high dimension models. We first study the fisher information matrix and derive Jeffrey's prior for the factor model. We extend the EM algorithm method for factor parameter estimation by applying the Jeffrey's prior, which turns to be more robust in the sense that risk would not be underestimated under small sample size. Next we extend the statistical factor model to be able to process empirical information.The fundamental(empirical) factor model and the statistical(hidden) factor model are widely used in factor analysis. The fundamental factor model is empirical, biased, and has small estimation variance. On the other hand, the statistical factor model is subjective, unbiased, but has a bigger estimation variance. In this paper, a new factor model called EH Factor Model (Empirical-Factor--and--Hidden-Factor Factor Model) is introduced to combine the two models under a unified framework. The EH model allows to include exogenous information to help reducing the number of parameters, and meanwhile it maintains a statistical factor structure so that the idiosyncratic variance is kept. In this way, it reduces the estimation variance and the bias. We also compare the EH model with a widely used hybrid approach, which firstly apply the fundamental factor model and then treat the residuals with the statistical factor model. Compare with this approach, The EH model does not require to assume that the column space of statistical factor exposures is orthogonal to the fundamental factor exposures, and is also shown to be more robust in a sense of less estimation variance and bias. | 100 pages
Recommended Citation
Dong, Xu, "New Development on Market MicroStructure and MacroStructure: Patterns of U.S. High Frequency Data and A Unified Factor Model Framework" (2013). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 3388.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/3388