TABLE 2.2 Numbers of archived ticks of main FX rates. Tick frequencies of main FX rates: (I) main rates against the USD, (2) main cross rates, and (3) main rates against historical currencies now replaced by the Euro (EUR).

Still on the wholesale market, but in contrast to other players, central banks can afford relatively large open positions and can thereby have a significant impact on the market in the long run. The different types of traders can of course be found within similar types of institutions.10

To illustrate the enormous amounts of available FX spot ticks, Table 2.2 displays the size and frequencies of ticks in the Olsen & Associates (O&A) database. The FX rates of this table are between major currencies, the first one of a currency pair being the "exchanged" currency whose value is expressed in the second currency (which can be called the numeraire currency). The analyzed periods have been chosen with respect to the transition of some European currencies such as DEM and FRF to the Euro (EUR) at the beginning of 1999. On the largest market, EUR-USD, more than 10,000 ticks per business day are available; that is an average of almost 10 ticks per minute which can rise to 30 or more ticks per minute during the busiest periods. The daily tick frequencies of Table 2.2 are averages. The values of the 1980s and the early 1990s were distinctly smaller than the values nowadays. In todays data feeds, some of the ticks contain little information if they are copies of ticks from other contributors (as explained in Section 2.2.3) or repeatedly posted ticks (see Section 4.2.2). Minor FX rates have fewer ticks than the rates in Table 2.2, very few ticks if the liquidity is low.

In contrast to daily or weekly data, collecting tick-by-tick quotes presents a number of practical problems such as transmission delays and breakdowns or

For example, Bank Negara of Malaysia was one of the most aggressive (short-term) speculators in the FX market for several years.

aberrant quotes due to human and technical errors. Therefore, it is important to implement a data cleaning filter to eliminate outliers. An extensive discussion of data cleaning is presented in Chapter 4.

2.2.2 Synthetic Cross Rates

FX rates between two currencies other than the U.S. Dollar (USD) are called cross rates. There are quotes for some important cross rates such as those in Table 2.2. For many other cross rates, there is little data or no data at all, either because the market for that cross rate is neglected by the data suppliers or because there is no direct market at all. In the second case, traders would go through a vehicle currency such as USD or EUR instead of making a direct transaction. A Canadian trader, for example, would obtain Japanese Yen (JPY) by buying USD from the USD-CAD market and selling USD on the USD-JPY market. The actual exchange rate in this case is

These formulas reflect the triangular relation between the three currencies USD, JPY, and CAD. If a direct market for JPY-CAD exists and its prices strongly deviate from this relation, the deviation can be profitably exploited through a set of riskless transactions. Such a strategy is called triangular arbitrage and leads to market adjustments that bring the prices back toward the relation of Equation 2.1. Traders are usally quick enough to make such arbitrage transactions before the prices strongly deviate from Equation 2.1. A trader calling market makers to execute an indirect transaction has to pay the bid-ask spreads of two markets, both USD-CAD and USD-JPY in our example. Both bid-ask spreads together may be higher than the bid-ask spread of a direct transaction.

In the case of cross rates with a direct market but bad data coverage, we are forced to compute synthetic cross rates through formulas such as Equation 2.1 which serve as proxies for the unknown direct rates. The two ticks used for the cross rate computation (a USD-CAD tick and a USD-JPY tick in the example of Equation 2.1) should be synchronous such that their time stamps deviate by no more than a few seconds or perhaps a minute. Otherwise, the synthetic cross rate is distorted by price moves in the time interval between the two ticks. The bid-ask spreads of the missing direct quotes can be expected to be lower than the synthetic bid-ask spreads. The data coverage for cross rates may only be bad during the active market hours of some time zones (e.g., due to the bad coverage of Asian markets by some data suppliers). In this case, we may have to mix quoted cross rate data with synthetic data (at certain daytimes).

2.2.3 Multiple Contributor Effects

The transactions of over-the-counter markets are between many individual institutions (banks and brokers). The market makers among these institutions publish

WPY/CAD.bid =

PUSD/CAD.bid />USD/JPY,ask

AlPY/CAD,ask =

PUSD/CAD.ask />USD/JPY,bid

(2.1)

their own price quotes. Data suppliers mix these data with the quotes of other contributors, thus creating a multicontributor data feed. Individual quotes are affected by the positions, views, and trading strategies of individual contributors, rather than behaving uniformly. Researchers using these data should be aware of this fact.

The FX spot market is the key example of a multicontributor market. The following multicontributor effects have been found in FX spot data:

Depending on their inventory position, market makers have preferences for either selling or buying. They publish new quotes to attract traders to make a deal in the desired direction so that either the bid or the ask quote is competitive. The other price of the bid-ask pair is pushed away to a less attractive region by adding or subtracting a rather large, nominal spread. This leads to high unrealistic quoted bid-ask spreads and a negative autocorrelation of returns at lags of around one minute as discussed in Section 5.2.1.

There are contributors of low reputation that abuse some quotes in attempts to manipulate the market into a desired direction.

FX quotes lag behind the real market prices. This is confirmed by FX traders we have interviewed and from comparisons to transaction data from electronic trading systems. A closer look shows that some leading contributors do not have a considerable delay, whereas many other contributors lag behind by more than a minute. This can be shown through a lead-lag correlation analysis of returns of contributor-specific time series.

Some contributors are laggards because they publish prices copied from the quotes of other contributors (e.g., moving averages of recent quotes with a tiny random modification). The motivation is to advertise the market presence of the contributor in the data feed (whereas true prices are negotiated over the telephone). These contributors often employ computers to publish fake quotes at high frequency. The described data-copying methods lead to lower data quality in general and lead to data-cleaning problems as discussed in Chapter 4.

Similar multicontributor effects are also found and expected in markets other than the FX spot market.

2.3 OVER-THE-COUNTER INTEREST RATE MARKETS

Two financial markets related to interest rates are over-the-counter (OTC) markets between individual banks.11 These are the spot interest rate (IR) market and the FX forward market.

11 This is similar to the interbank FX market.