the price levels became lower (Muller and Sgier, 1992). As explained in Section 3.2.5, spreads mainly depend on the cost structure of the market making banks and the habits of the market. Goodhart and Curcio (1991) have shown that individual banks usually quote two or three different spreads. Market makers who want to attract buyers more than sellers, or the other way around, tend to publish a skewed quote where only either the bid or the ask price is competitive and the other price is pushed away by a spread of conventional size, often 5 or 7 basis points. When they are uncertain about the direction the price should take, they may quote larger spreads with conventional values such as 10 or 15 (Lyons, 1998). Because different banks have different conventions and market situations change over time, the distribution of spreads has 4 or 5 peaks instead of 2 or 3.

A possible way to approximately model the real spreads, that is the difference between traded bid and ask prices, could be an analysis of the market microstructure which is discussed in detail by Flood (1991). Such a real spread model would analyze the microoscillations of (almost) simultaneous prices from different market makers. The effective spread would be something like the difference between the lowest ask and the highest bid prices currently quoted by any market maker-a model that would complement the effective price model proposed in Section 5.2.1. We did not try to set up such a subtle model, although we think that this would be the only way to overcome the limitations of quoted spreads. In a recent paper, Hasbrouck (1998) precisely proposes a market microstructure model for the clustering of the spreads based on a similar idea of a latent continuous efficient price.

Although the distribution of the spreads is discrete and consistent with theory (Admati and Pfleiderer, 1988; Subrahmanyam, 1991) market makers will cover themselves by conventional larger spreads in periods of higher risk such as in the release of important news (Goodhart, 1989), the closing or opening of markets (Bollerslev and Domowitz, 1993) and lunch breaks, (Muller et al, 1990). More generally, the size of the spread is inversely related to market activity as measured by the tick frequency or the mean hourly volatility (Muller et al., 1990). The size of the spread is directly related to the (instantaneous) volatility, which also measures the risk (Bollerslev and Domowitz, 1993).

In Figure 5.2, very different pictures emerge from the quoted spreads, which are only indicative, and the spreads as obtained from the electronic dealing system Reuters Dealing 2000-2. The different behaviors of the spread constitute the most pronounced difference between quoted prices and transaction prices. In Figure 5.2, the spread of actual transaction prices is uniformly distributed as one would expect. In their paper, Goodhart et al. (1995) note that, contrary to spreads, the volatility of middle prices does not exhibit substantial differences when transaction prices are used instead of quotes.

In the case of exchange-traded instruments such as Eurofutures (IR futures), there is no well-defined spread because the bid and the ask quotes are not synchronized and, depending on the market state, there may be only bid quotes

or only ask quotes for a while. Nevertheless, a spread can be computed from bid and ask quotes that are few seconds apart. This effective spread is usually very small, typically less than one basis point on the Eurofutures market (Ballocchi et al, 1999b), which represents relative spreads of the order of 10~4 according to the definition in Equation 3.12. Similar values are found for bond futures traded on the Deutsche Termin-Borse (DTB) (Franke and Hess, 1997).

5.2.3 Short-Term Triangular Arbitrage

The extremely short-term dynamics of price processes is also reflected in the significant predictive power of the USD-DEM in contrast to the other currencies (Goodhart and Figliuoli, 1991). A short delay is needed before traders in smaller currencies adjust themselves to the patterns of the two leading currencies. It is an effect comparable to the one wc described in Section 5.2.1 for the positive autocorrelation of high-frequency returns of stock indices. Eben (1994) also finds evidence of triangular arbitrage opportunities at very high frequencies arising from very short-term trend reversals between two USD-rates, which are not yet reflected in the quoted cross rates. Although the detection of triangular arbitrage opportunities is rather easy and quick with a unique vehicle currency, it takes more time when the rates between two vehicles (e.g., USD and DEM) change (Suvanto, 1993; Hartmann, 1998).

Triangular arbitrage opportunities detected in quoted data do not necessarily reflect riskless profit-taking opportunities in real markets. The transaction costs may exceed the profits and the transaction prices may adjust more quickly than the quotes.

5.3 INSTITUTIONAL STRUCTURE AND EXOGENEOUS IMPACTS

5.3.1 Institutional Framework

An example of an institutional framework is the European Monetary System (EMS) introduced in the 1990s to keep some intra-European FX rates within certain bands. An intradaily analysis of FX rates within the EMS gives some insights into the distinct characteristics of this monetary system at a time when the bands were still quite narrow. As illustrated in Figure 5.3 (b), the EMS achieved a smaller drift exponent of the scaling law.

The scaling law relates the mean absolute return E[\r\] observed over time intervals of a certain size to the size At of these intervals: E[\r\] = const (At)D. The exponent D is called the drift exponent and empirically estimated using data samples. Low drift exponents indicate that the EMS successfully reduced the size of returns over large time intervals as compared to the volatility of short-term returns. A further, detailed discussion of drift exponents and their empirical estimation can be found in Section 5.5.

FIGURE 5.3 Drift exponents of the scaling law as a function of time, empirically estimated for yearly samples, (a): Drift exponents of freely floating rates against the USD, DEM (•), FRF ( ), JPY (*). (b): Drift exponents of EMS rates against the DEM, ITL (□) and FRF (O).

When the Italian Lira (ITL) left the EMS in 1992 and the EMS bands of the French Franc (FRF) were broadened in 1993, the values of the drift exponents went up and approached those of freely floating rates, as can be seen in Figure 5.3.

The drift exponent and the long-term volatility under the EMS were reduced, however, at the cost of a larger probability of extreme events. This is further explained in Section 5.4.2. The statistical analysis of EMS rates shows that institutional setups such as the EMS can be distinguished from freely floating markets by purely statistical criteria in a robust way, independent of assumptions on the generating-process.2

Another effect of the market framework can be seen in other financial high-frequency data such as interbank spot interest rates. In this market, money market quotes coming from East Asia are systematically higher than those from Europe or America. Figure 5.4 clearly indicates that for USD 3-month money market rates (spot interest rates collected from Telerate) the last bid quote before 2 a.m. GMT (Greenwich Mean Time) almost always exceeds the last bid quote before 8 p.m. GMT. On average, the early quote is larger by one-eight of a percent. The interest rate intraday seasonality is caused by a geographical market segmentation between East Asia on one side and Europe and America on the other side. This segmentation is justified by market practitioners as being due to institutional constraints and credit risks, making it less appealing on average for a European bank to place a deposit with an East Asian counterparty than with a European counterparty. The temporary difficulties in the Japanese banking sector were a likely cause of the segmentation. The segmentation became very pronounced in the last half of 1995 and again during the "Asian crisis" in 1998 (with interest rate deviations of about

2 See Svensson (1992) for a review of the literature on the modeling of target zones, and in particular, of the European Monetary System.