Elements of Volatility at High Frequency

Volatility is central in options pricing and risk management. It reflects the uncertainty of investors and the inherent instability of the economy. Time series methods are among the most widely applied scientific methods to analyze and predict volatility. Very frequently sampled data contain much valuable information about the different elements of volatility and may ultimately reveal the reasons for time varying volatility. The use of such ultra-high-frequency data is common to all three essays of the dissertation. The dissertation belongs to the field of financial econometrics. The first essay uses wavelet methods to study the time-varying behavior of scaling laws and long-memory in the five-minute volatility series of Nokia on the Helsinki Stock Exchange around the burst of the IT-bubble. The essay is motivated by earlier findings which suggest that different scaling laws may apply to intraday time-scales and to larger time-scales, implying that the so-called annualized volatility depends on the data sampling frequency. The empirical results confirm the appearance of time varying long-memory and different scaling laws that, for a significant part, can be attributed to investor irrationality and to an intraday volatility periodicity called the New York effect. The findings have potentially important consequences for options pricing and risk management that commonly assume constant memory and scaling. The second essay investigates modelling the duration between trades in stock markets. Durations convoy information about investor intentions and provide an alternative view at volatility. Generalizations of standard autoregressive conditional duration (ACD) models are developed to meet needs observed in previous applications of the standard models. According to the empirical results based on data of actively traded stocks on the New York Stock Exchange and the Helsinki Stock Exchange the proposed generalization clearly outperforms the standard models and also performs well in comparison to another recently proposed alternative to the standard models. The distribution used to derive the generalization may also prove valuable in other areas of risk management. The third essay studies empirically the effect of decimalization on volatility and market microstructure noise. Decimalization refers to the change from fractional pricing to decimal pricing and it was carried out on the New York Stock Exchange in January, 2001. The methods used here are more accurate than in the earlier studies and put more weight on market microstructure. The main result is that decimalization decreased observed volatility by reducing noise variance especially for the highly active stocks. The results help risk management and market mechanism designing.

Fast in-memory XPath search using compressed indexes

A large fraction of an XML document typically consists of text data. The XPath query language allows text search via the equal, contains, and starts-with predicates. Such predicates can be efficiently implemented using a compressed self-index of the document's text nodes. Most queries, however, contain some parts querying the text of the document, plus some parts querying the tree structure. It is therefore a challenge to choose an appropriate evaluation order for a given query, which optimally leverages the execution speeds of the text and tree indexes. Here the SXSI system is introduced. It stores the tree structure of an XML document using a bit array of opening and closing brackets plus a sequence of labels, and stores the text nodes of the document using a global compressed self-index. On top of these indexes sits an XPath query engine that is based on tree automata. The engine uses fast counting queries of the text index in order to dynamically determine whether to evaluate top-down or bottom-up with respect to the tree structure. The resulting system has several advantages over existing systems: (1) on pure tree queries (without text search) such as the XPathMark queries, the SXSI system performs on par or better than the fastest known systems MonetDB and Qizx, (2) on queries that use text search, SXSI outperforms the existing systems by 1-3 orders of magnitude (depending on the size of the result set), and (3) with respect to memory consumption, SXSI outperforms all other systems for counting-only queries.