Before closing this page of gratitude, we do not want to forget Dina Weid-mann and Elisa Guglielmo, who cooked so many fine dishes with the Italian touch and make O&As famous "Friday family lunches" a genuine gourmet experience. Faced with mountains of data to unravel, this lovely tradition warmed the soul. Grazie.

Michel M. Dacorogna Ramazan Gencay Ulrich A. Muller Richard B. Olsen Olivier V. Pictet

INTRODUCTION

i. i markets: the source of high-frequency data

A famous climber, when asked why he was willing to put his life in danger to climb dangerous summits, answered: "Because they are there." We would be tempted to give the same answer when people ask us why we take so much pain in dealing with high-frequency data. The reason is simple: financial markets are the source of high-frequency data. The original form of market prices is tick-by-tick data: each "tick" is one logical unit of information, like a quote or a transaction price (see Section 2.1). By nature these data are irregularly spaced in time. Liquid markets generate hundreds or thousands of ticks per business day. Data vendors like Reuters transmit more than 275,000 prices per day for foreign exchange spot rates alone.

Thus high-frequency data should be the primary object of research for those who are interested in understanding financial markets. Especially so, because practitioners determine their trading decisions by observing high-frequency or tick-by-tick data. Yet most of the studies published in the financial literature deal with low-frequency, regularly spaced data. There are two main reasons for this. First, it is still rather costly and time-consuming to collect, collate, store, retrieve, and manipulate high-frequency data. That is why most of the available

financial data are at daily or lower frequency. The second reason is somehow more subtle but still quite important: most of the statistical apparatus has been developed and thought for homogeneous (i.e., equally spaced in time) time series. There is little work done to adapt the methods to data that arrive at random time intervals. Unfortunately in finance, regularly spaced data are not original data but artifacts derived from the original market prices. Nowadays with the development of computer technology, data availability is becoming less and less of a problem. For instance, most of the exchanges and especially those that trade electronically would gladly provide tick-by-tick data to interested parties. Data vendors have themselves improved their data structures and provide their users with tools to collect data for over-the-counter (OTC) markets. Slowly, high-frequency data are becoming a fantastic experimental bench for understanding market microstructure and more generally for analyzing financial markets.

That leaves the researcher with the problems of dealing with such vast amounts of data using the right mathematical tools and models. This is precisely the subject of this book.

1.2 methodology of high-frequency research

From the beginning, our approach has been to apply the experimental method which has been highly successful in "hard" sciences.1 It consists of three steps, the first one being to explore the data in order to discover the fundamental statistical properties they exhibit with a minimum set of assumptions. This is often called finding the "stylized facts" in the econometric or finance literature. This first step was in fact not so important in the economic literature, because the sparse-ness of data made it either relatively simple or uninteresting due to the statistical uncertainty.

The second step is to use all of these empirical facts to formulate adequate models. By adequate models, we do not mean models that come from hand-waving arguments about the markets, but rather models that are directly inspired by the empirical regularities encountered in the data. It is the point where our understanding of market behavior and reality of the data properties should meet. There have been many debates between the time series approach and microstructure approach. The first one relying more on modeling the statistical properties of the data and the latter concentrating on modeling market behavior. Both approaches have their value and high-frequency data might be able to reconcile them by enabling us to actually test the microstructure models, Hasbrouck (1998); Rydberg and Shephard(1998).

The third step, of course, is to verify whether these models satisfactorily reproduce the stylized facts found in the data. The ultimate goal is not only a good descriptive model but the ability to produce reasonable predictions of future movements or risks and to integrate these tools into practical applications, such

1 We refer here to experimental sciences such as physics, chemistry, or biology.