Some important spot markets are over-the-counter markets between individual institutions (banks), whereas many derivatives are traded at exchanges. However, this is not a general rule.

2.1.2 Futures Markets

In some cases such as most interest rates and commodities, futures markets have a higher liquidity and volume than the underlying spot markets and produce better high-frequency data. The following description of futures markets is quite general, and special features of particular futures markets are discussed in other sections.

Futures contracts are derivatives of an underlying asset, which can be defined as an agreement between two parties to buy or sell an asset at a certain time in the future for a certain price, Hull (1993). At this expiry time, the underlying asset has to be delivered according to settlement rules, after which the contract no longer exists. The expiry dates are regularly scheduled, often in a quarterly sequence. The contract with the nearest expiry is called the first position, the following contract the second position, and so on.

Most futures are traded at exchanges. Trading is typically geographically localized. There is no 24-hour trading, there are rigidly defined opening hours, although the trend is to effectively lengthen the active hours (e.g. with after-hours sessions). Given that futures contracts are exchange traded and each transaction is recorded centrally, futures markets offer a high price transparency. The historical data always include tick-by-tick transaction prices and, depending on the data source, bid and ask quotes and sometimes information on volumes and the flow of orders from the clients of the exchange.

The structure of many futures markets has changed due to the rapid growth of market volumes, some mergers of exchanges, and the shift from floor trading (open outcry) to electronic trading. For some researchers, this shift has been an object of study in itself.

All clients buying or selling futures contracts have to put some money in a collateral account. This account covers the counterparty default risk of the exchange. If the futures prices move to the disfavor of a client, the amount of money on the collateral account may no longer cover the risk, and the exchange will tell the client to increase it through a "call for margin." If the client fails to do this, the futures contract is terminated at its current market value. The flow of money to the collateral account (which earns some interest in its own right) makes the exact bookkeeping of returns (and risks) rather complicated, but this can be ignored in most studies.

The time series of prices coming from a single futures contract is not sufficiently long for certain statistical studies. Moreover, the behavior of a contract changes when approaching expiry and its price volatility systematically grows or shrinks according to the nature of the underlying asset. For these reasons, it is sometimes necessary to construct long samples joining several contracts together. Different empirical prescriptions are used by analysts and traders to join price

histories of several futures contracts with successive expiries. Such prescriptions are typically based on rollover schemes - that is, they attempt to replicate the behavior of a trader holding a contract and switching ("rolling over") to the next contract before the expiry of the current contract. Section 2.5.2 gives such an example.

The opening hours of futures markets are sometimes modified, as those of other centralized markets. Long samples may extend over periods with different fixed opening hours. This fact leads to some difficulties in intraday studies, especially those related to daytime. Researchers should be aware of this and know the history of opening hours.

2.1.3 Option Markets

Option prices are very volatile and depend on parameters such as the strike price, the base spot price, and the expiry date. There are many types of options. The options markets are often too volatile for studying consistent time series over long samples and are not the subject of this book-except for the implied volatility aspect.

Unlike option prices, implied volatility figures are slowly changing over time. They are computed from option prices through the formulas introduced by Black and Scholes (1973) and some refined methods introduced later. The implied volatility figures provided by data vendors usually refer to at-the-money options (where the strike price is not far from the base spot price). For some markets, these data are available in high frequency with several quotes per day. Implied volatility can be interpreted as the markets forecast of the volatility of the underlying asset for the time period until expiry. Therefore, time series of implied volatility are interesting especially in comparison to historical or realized volatility computed from time series of underlying assets.

2.2 FOREIGN EXCHANGE MARKETS

The foreign exchange (FX) market is the largest financial market. Already in April 1992, its "traditional" part (FX spot and FX forward market, excluding the newer derivatives) had a daily net-net3 turnover of 832 billion U.S. Dollar (USD) (Bank for International Settlements, 1993) which was more than the total non-gold reserves (USD 555.6 billion) of all industrial countries in 1992 (International Monetary Fund, 1993). Since that time, the FX net-net turnover had grown to USD 1190 billion in April 1995 and to USD 1500 billion in April 1998 (Bank for International Settlements, 1999).

The FX spot market produces high-frequency data that played and still play a central role in high-frequency finance. Unlike other data, these data are available over long sampling periods in high frequency, 24 hours per working day. The market is highly liquid and symmetric as both exchanged assets are currencies.

3 This figure is adjusted for both local and cross-border double-counting.

Due to these favorable characteristics, new facts have often been found in FX spot data, and FX studies have served as a role model for the investigation of other high-frequency data with less favorable properties.

Since the beginning of the 1990s, academic researchers have been gaining new insights into the behavior of the FX markets through analyzing intraday data. Daily data, which were much used in the 1980s represent only a small subset of the information available at intraday frequencies, as they are only the average of a few intraday prices quoted by some large banks at a particular daytime. The number of data points available for intraday is larger by a factor of 1000.

On the basis of this information set, there is a rapidly growing body of literature in the study of the intraday FX markets, which opens new directions for understanding of financial markets and widening of concepts such as risk management or market efficiency. The analysis of intraday data also leads to insights into the market microstructure where it is possible to study the behavior of intraday traders, whose operations account for more than 90% of the FX market volume.

The stylized facts found for intraday FX rates shed some new light on different modeling approaches to the FX market.4 Research studies have shown that known and well-accepted empirical regularities of daily or weekly data do not always hold up in intraday analysis. Looking at intraday data, the homogeneity of market agents (which is a working hypothesis for studying daily, weekly, or low-frequency data) disappears. A new wealth of structure is uncovered that demonstrates the complexity of the FX market at the intraday frequency. This complexity can be explained by the interaction of market agents with heterogeneous objectives resulting from different geographical locations, the various forms of institutional constraints, and risk profiles. This evidence will be presented in several chapters of this book. Indeed, the heterogeneous structure of intraday data may explain the fact that practitioners have effectively used methods of "technical analysis" over many years now. These intuitively designed methods try to take advantage of the interaction of different components of the markets, see Dunis and Feeny (1989); Neftci (1991); Surajaras and Sweeney (1992); Taylor and Allen (1992); Pictet etal. (1992); Levich and Thomas (1993b); Brock etal. (1992); Gencay and Stengos (1998) and Gencay (1998a,b, 1999); Gencay etal. (2001c, 2002).

The FX spot market is presented in Section 2.2.1. Aside from the spot market, there is also the over-the-counter FX forward market treated in Section 2.3.2 and the markets for FX futures and FX options. The contracts of these markets refer to a time period in the future, therefore they are affected by interest rate levels.

Exchange-traded FX futures follow the description of Section 2.1.2 and are not discussed here; their market volume is much lower than that of the FX spot market and the over-the-counter derivative markets, particularly the FX forward market.

As mentioned in Section 2.1.3, time series of implied volatility are available from the FX option markets. These are interesting objects of study, together with realized or historical volatility computed from FX spot rates.

4 For surveys on the FX market at the daily or weekly frequencies, see, for example, the surveys of Mussa (1979); Hsieh (1988); Baillie and McMahon (1989), and de Vries (1992).