Intraday Evidence on International Market Integration∗

Burton Hollifield† Patrik Sand̊as‡ Andrew Todd§

December 15, 2014

Abstract

We study the integration of limit order books for equities that trade in parallel limit

order books. The different markets trade the same securities in different currencies in

parallel electronic limit order books. With two parallel books the inside quotes can

essentially be in six different states. We document the frequency and duration of

periods when the order books are in states deviating from the law of one price. On

a typical day around ten of these states occurs and last for between less than ten

seconds (Nokia) to close to two minutes (SAS). The typical deviations are less than

100 euros. Deviations from one price are correlated across all sample stocks indicating

that FX movements play an important role in triggering these situations. Overall we

find that the deviations from the law of one price are small and quickly disappearing

despite occurring quite frequently. We take this as evidence of a high degree of market

integration within the NASDAQ OMX Nordic exchanges.

JEL Classifications: G10; G14; G15

Keywords: Cross Listed; Arbitrage; Law of One Price; Limit Order Book

∗NASDAQ OMX for the data and the McIntire Foundation for financial support.†Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA 15213. Phone: 412-268-6505,

Email: burtonh@andrew.cmu.edu‡McIntire School of Commerce, University of Virginia, Charlottesville, VA, 22904. Phone: 434-243-2289.

Email: patriks@virginia.edu. Sand̊as is a SIFR research affiliate.§School of Engineering, University of Virginia, Charlottesville, VA, 22904. Email: aet6cd@virginia.edu.

1. Introduction

Deviations from the law of one price should be brief and short for cross listed securities

since they are claims to identical future cash flows. Whether that is true or not is usually

interpreted as a test whether the markets are fully integrated or not. We examine the

integration of the market for stocks that are cross-listed within the Nasdaq OMX Nordic

Exchange. These are not depositary receipts but shares that are claims to the same cash

flow denominated in different currencies.

The main friction is that they trade in different currencies; Euros, Swedish Kronor or

Danish Kronor. For example, SAS Scandinavian Airlines, is listed on both the Stockholm

and the Copenhagen stock exchanges and trade on the same platform with a large overlap

among the member firms that trade the stock. It is, however, quoted and trade in Danish

Kronor in Copenhagen and in Swedish Kronor in Stockholm. For local investors that is

enough of a friction to make the market segmented but the question is if the presence of

institutions that monitor prices and quotes in both markets is enough to effectively make

the market fully integrated. The discrete tick size combined with the different currencies is a

friction for all members. We seek to quantify how often and for how long and by how much

the law of one price is violated in these markets. There is no legal obligation to execute order

in a different market even if a more favorable quote was available. In other words there is

no problem legally with trade-throughs. This is in general true for all European markets.

We define states in which the quotes in two markets are either best bid above best ask or

vice versa, when translating the quotes to the same currency, as deviations from the law of

one price. We establish that states that constitute deviations from the law one price (LOP)

account for anywhere from about 6% of the time to closer to 10% of the time. In terms of

how often the order books are in such states we establish that it occurs around ten times

per day or more frequently. How long each state of deviation from LOP lasts varies across

stocks. For Nokia it lasts less than ten seconds whereas for SAS it lasts almost two minutes

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on average. The size of these deviations can often be categorized as too small to matter,

less than 100 euros. But for every stock there are observations of deviations that are several

hundred euros which would constitute actionable arbitrage opportunities. Given that the

larger deviations are infrequent and the deviations typically short lived we take our evidence

as supporting market integration.

A natural follow-up question is how the LOP violations come about and how the market

corrects them. By examining the euro price difference from two markets regardless of its

size we can establish whether these deviations occur at the same time as would be the

case if they are triggered by foreign exchange movements or whether we need to look for

idiosyncratic demand and supply shocks. We find that the deviations in price are cross

correlated suggesting that the foreign exchange shifts are one driver of the deviations from

LOP. We further document a consistent correlation between the exchange rate and the

deviations.

We are also interested in how the market transitions away from states with LOP viola-

tions. Our intuition is that from a state with a LOP violation you would transition to one

in which the quotes straddle for the two markets. We establish that the market typically

transitions into one of the states in which each market has one of the best/inisde quotes as

opposed to the states with one market having both the best bid and the best ask quotes.

This confirms our intuition for the dynamics of the limit order books.

1.1 Institutional Setting

NASDAQ OMX Nordic operates the stock exchanges in Stockholm, Helsinki and Copen-

hagen. The exchanges operate with the same exchange technology and with a large number,

but not all, members being members of all three exchanges. The table 2 reports the distribu-

tion of exchange memberships across the, at the time, four exchanges within the NASDAQ

OMX Nordic Exchanges, this add Iceland which does not have a cross listing for our sam-

2

ple period. Note that a significant fraction of the exchange member firms based on market

shares are members of the three major exchanges. There are a few purely local member

firms in all three markets and a handful of exchange member firms that are members of

some combination of two exchanges.

Since the three exchanges have different currencies the tick sizes become a non-trivial

issue. Table 3 tabulates the tick sizes by stock, exchange, in the native currency. For our

sample period the DKK/EUR exchange rate was around 7.45 and the SEK/EUR exchange

rate was around 9.45. Naturally a discrete tick size grid that is fixed combined with any

continuous exchange rate causes some temporary advantages for a market and this is no

exception. Hence through the discrete tick size the foreign exchange rate shifts are not

trivially incorporated into the quotes. If one factors in the other reasons why someone might

place a bid at a higher price or ask at a lower price because of a desire to make a transaction

occur there can naturally be situations where the quotes differ once converted to the same

currency.

While it is not our main focus it is important to note that each market has, in almost

all cases, a natural captive audience of retail investors who prefer to trade their securities

in their own home currency. That creates a situation in which a relatively coarse price

grid perhaps make the order flow skewed towards one type of investors in one exchange and

different segments of investors go to the market that naturally has a tighter tick size. This is

to say that there may be a clientele for every market even in a situation in which textbook

microeconomic analysis might say one exchange cannot possibly survive.

1.2 Brief Literature Review

A classic paper on cross listed securities is Kleidon and Werner (1996). Suarez (2005)

examine French and American stocks that are cross listed in the respective markets. The

analysis focus on quote data. Alsayed and McGroarty (2011) examines how pairs trading

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can be used to exploit mis-pricing and is typically more effective than conventional arbitrage

strategies. Kaul and Mehrotra (2000) analyze cross listed securities in North America.

Foucault and Menkveld (2008) look at a case similar to ours with Dutch stocks being cross

listed or traded in London. One difference between Foucault and Menkveld (2008) and our

situation and many of the other studies is that in our case it is the same exchange operator

who runs all markets so one cannot argue it is primarily a battle for market share. It is true

that one might argue that there is always potential competition by other platforms that may

be driving things. But by and large our situation is one where one exchange operator decides

in the case of Nordea to run three parallel markets. The historical reason is that Nordea

Bank is a results of a number of bank mergers and hence it naturally has a shareholder base

who prefers to trade the stock in their own local currency. Ultimately it appears to use that

the different currencies is that real barrier that makes the parallel markets run by the same

exchange operator make any economic sense.

2. Data

Our sample consists of order book and trade data for stocks cross listed within the

NASDAQ OMX Nordic market. Specifically, we include all stocks that are cross-listed or

cross-quoted across the Copenhagen, Helsinki, and Stockholm stock exchanges. Our foreign

exchange data for the respective currencies was obtained from Olsen and Associates, for

Danish and Swedish Krona and euro. All order book and transaction data that is quoted in

Danish or Swedish Kronor are converted to euros.

Table 2 report how the different exchange members are distributed across different ex-

changes in terms of their exchange memberships. We are investigating the degree of market

integration and hence a natural question is how integrated the markets are in terms of ex-

change memberships. One could imagine a set of three markets where most members are

‘local’ and integration would occur mainly through the few firms that operate across the

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markets.

Tabele 2 shows that the three markets are highly integrated in the sense that exchange

member firms that operate across all three markets account for a lot of the volume and

the number of transactions. There are also a relatively large number of such members, 47

firms are members of the Helsinki, Stockholm, and Copenhagen exchanges and another 23

are members of either Stockholm and Helsinki or Stockholm and Copenhagen. There are

45 firms that are local members only in one of the three markets but they also account for

a relatively small share of the turnover. This picture changes a bit if one examines large

capitalization stocks versus small and medium but all our sample firms are in the larger

category for which these statistics are quite representative.

Table 1 shows how our sample of cross listed stocks are distributed across the three

NASDAQ OMX Nordic exchanges. Stockholm is involved in all cross listed securities, with

Helsinki closely behind involved in all but SAS.

3. Methodology

Conversion of order book quotes and transaction prices from native currency to euros.

Figure 1 illustrates how different constellations of bid and ask quotes translate into dif-

ferent states. Table 4 provides the complete list and definition of the states that completely

describes the configuration of best bid and ask quotes for two markets. Figures ?? and 3

show how the quotes transition between constellation that we map into our definitions of

states.

The states of the market and various quantities of interest are calculated after all prices

are converted to euros. The FX data has millisecond resolution whereas the order book data

from NASDAQ OMX has second resolution. In order to reduce distortions related to the

discrepancy in time stamps the order book events occurring within a second are distributed

uniformly within that second prior to performing the currency translation. (See Holden and

5

Jacobs (2014)).

The paper reports on a number of quantities including the difference between the mid-

quotes in each market and the size of arbitrage opportunities. The size of an arbitrage

opportunity in state 6 is defined as (bid1 − ask2) × min{Depth(bid1),Depth(ask2)} where

Depth(p) is the depth available at price p. The size of an arbitrage opportunity in state 7

is (bid2 − ask1)×min{Depth(bid2),Depth(ask1)}. The subscript 1 represents the market in

Stockholm and the subscript 2 represents the market in Helsinki (with the exception of SAS,

in which case subscript 2 is for Copenhagen).

4. Results

In this section we examine the frequency, duration, number of unique observations of

the law of one price and the size distribution of the deviations. We start by examining the

frequency of different states including the deviations from the law of one price.

4.1 Frequency of Deviations from LOP

Table 5 reports the distribution of time spent in the eight different states for the stocks

in our sample. From rows 6 and 7 the average stock spends around 8% in states in which

the best bid and ask quotes deviate from the law of one price.

In terms of the different states that satisfy the law of one price, i.e., 2, 3, 4, and 5,

we learn that for some of the stocks, Nokia, Stora Enso, and Tieto and Ericsson all have

one dominant market in terms of displaying the inside spreads. For example, for Ericsson

Stockholm displays the inside spread roughly 87% of the time and for Stora Enso Helsinki

displays the inside spread 54% of the time. For SAS and Telia Sonera we observe that both

Helsinki and Stockholm displays one of the inside quotes more than 50% of the time, in other

words, a mixed state is the rule for these two stocks.

Interestingly Nokia, which has the tightest inside spread and active trading, displays

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quotes that violate the law of one price more often than the other stocks in our sample.

Below we examine how long these situations last and how sizable they are.

4.2 Duration of Deviations from LOP

Table 7 reports the average duration of each visit to each state by stock. States 6 and 7

which are the states that involve deviations from LOP do not last very long. The deviations

last on average less than 10 seconds for Nokia and a bit over twenty seconds for Nordea but

they typically last longer for the other stocks. For SAS they last on average just under two

minutes on average.

Table 6 report the number of unique visits to each state which tells us how often different

states are visited. For example, from Table 7 we might conclude that the stocks spend some

time in state 1 which is the state with the market now being established. Table 6 shows

that that states is rarely visited. This is true with the exception of Ericsson which has the

most skewed cross listed with very little activity in Helsinki.∗ Note that the distribution

of the unique states visited (the bottom half of the table) supports the durations results in

that typically more than four percent but less than ten percent of the time is spent in the

deviation from LOP states 6 and 7.

4.3 Size of Deviations from LOP

Table 9 and Table 10 reports the empirical distribution of the size of the deviations

from law of one price. The majority of the deviations are less than 100 euros. But a

small fraction of the deviations are larger than 100 euros. The size of the deviations from

LOP is important for interpreting the evidence. Figures 4—Figure 6 plot the frequency

distributions of deviations from LOP. In the figures, positive observations are state 6 and

negative observations are state 7. The vast majority of observations entail deviations that

∗We are investigating whether there is a related reason for the market not being established, for example,there being no quotes in Helsinki which would make the cross listed market not established.

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are within plus minus 100 euros but occasionally the deviations from LOP are a few hundred

euros. We take into account the price deviations multiplied by the lesser of the depths

in question to quantity the deviation in euros. What is interesting is the skewness in the

three frequency distributions; the Nokia distribution is left skewed, the Telia Sonera is right

skewed and the SAS more symmetric. It would be interesting to examine if the pattern in

the distribution of deviations from LOP directly mirror the distribution across states with

Nokia and Telia Sonera representing more polar cases and SAS an intermediate case with

both markets occasionally posting the inside spread and the two markets often splitting the

inside quote position.

4.4 Transition Probability Matrices

It is of interest to know how stocks transition from different states. In particular, when

we observe deviations from LOP it seems plausible that the quotes would next transition to

a state where the quotes are straddled, state 3 and 4, and states 2 and 5 would be less likely

next states. Table 11 reports the transition probabilities for the different states for all stocks

using event based sampling.

4.5 Common Factors in the Deviations from LOP

Are the deviations from LOP driven by foreign exchange rate moves or are they driven by

‘local’ limit order book shifts? They are probably driven by both sources of shocks to some

extent but they can to some extent be disentangled. Foreign exchange market movements

are exogenous to any one or all of our sample stocks order book dynamics. Hence it should be

possible to pin down how much of the deviations can be explained by shifts in the SEK/EUR

and DKK/EUR exchange rates. In Table 13 we correlate the deviations from perfect parity in

the cross-listed stocks price across the different stocks focusing on the Stockholm and Helsinki

pairs of cross listings and the SEK/EUR exchange rate. By looking at a continuous variable

that should be centered around zero and quickly reverting back to zero the statistical analysis

8

becomes more straightforward than if we looked at the discrete states and state transitions.

Note that deviations from LOP always means that the variable is away from zero and LOP

approximately holds as we get closer to zero.

An interesting regularity is that the deviations are positively cross correlated across

all stocks. This indicate that foreign exchange movements do contribute to some of these

deviations. It also means deviations occur partly at the same time.

The fact that the correlation is not higher than it is must mean that idiosyncratic demand

and supply imbalances hitting different limit order books at different times matter as well.

The bottom row of Table 13 reports the correlation between the deviation in the prices

quoted at the two markets and the SEK/EUR exchange rate. The correlations have the

same sign and all show that foreign exchange shifts contribute to the deviations from LOP

that we have documented above.

5. Conclusion

We examine the order flow and trade dynamics for stock that are cross listed on the

NASDAQ OMX Nordic Exchanges. The most common pairing of exchanges is Stockholm

and Helsinki with six stocks and two stocks are traded on the Stockholm and the Copenhagen

exchanges. The three exchanges are operated by the same exchange operator, NASDAQ

OMX, and are all located in EU member countries. The currency, however, is different in all

three markets, euro, Swedish Kronor, and Danish Kronor. This friction appears to be the

main driver behind violations of the law of one price. Different exchange rate levels create

relative advantages and disadvantages for exchanges but they are slow moving. Sudden

exchange rate shift may cause the best quotes to be mis-aligned for a period of time and in

principle presents the market with arbitrage opportunities.

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References

Alsayed, Hamad, and Frank McGroarty, 2011, Arbitrage and the law of one price in themarket for american depositary receipts, Unpublished Manuscript .

Foucault, Thierry, and Albert J. Menkveld, 2008, Competition for order flow and smartorder routing systems, Journal of Finance 68, 119–158.

Kaul, Aditya, and Vikas Mehrotra, 2000, In search of international integration: An exam-ination of intraday north american trading of canadian dually listed stocks, UnpublishedManuscript .

Kleidon, Allan, and Ingrid Werner, 1996, U.k. and u.s. trading of british cross-listed stocks:An intrday analysis of market integration, Review of Financial Studies 9, 619–644.

Suarez, E. Dante, 2005, Arbitrage opportunities in the depository receipts market: Myth orreality?, Journal of International Financial Markets, Institutions and Money 15, 469–480.

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Table 1: Our Sample The table reports the securities in our sample and on which marketthey are traded.

Name of Firm Helsinki Stockholm CopenhagenNordea Y Y YStora Enso Y Y NTelia Sonera Y Y NTieto Y Y NSAS N Y YNokia Y Y NEricsson Y Y N

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Table 2: Distribution of Member Firms Across Exchanges The table reports thenumber of members that are members of all three exchanges or some combination of thethree along with the total market share in terms of turnover and number of trades in May2008 and from January to May 2008 for those groups. The exchanges are labeled as follow:Helsinki=H; Stockholm=S; Copenhagen=C.

Exchange Number of Turnover Number of TradesMemberships Firms May 2008 Jan-May 2008 May 2008 Jan-May 2008HSC 47 78.24% 76.52% 79.87% 78.75%HS 16 13.82% 16.48% 12.13% 13.91%SC 7 3.09% 2.53% 3.10% 2.75%C 25 3.58% 3.06% 3.01% 2.70%S 17 0.40% 0.37% 0.66% 0.62%H 3 0.75% 0.92% 1.21% 1.24%

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Table 3: Tick Size The table reports the tick size in the currency for each venue. Theapproximate exchange rates are SEK/EUR=9.45 and DKK/EUR=7.45

Name of Firm EUR SEK DKKNordea 0.01 0.10 0.25Stora Enso 0.01 0.25Telia Sonera 0.01 0.10Tieto 0.01 0.25SAS 0.25 0.10Nokia 0.01 0.25Ericsson 0.01 0.10

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Table 4: Orientation of bids and offers The table reports the orientation of the best bidand offer prices once they are converted into Euros. The subscript 1 represents the marketin Stockholm and the subscript 2 represents the market in Helsinki (with the exception ofSAS, in which case subscript 2 is for Copenhagen). The markets are crossed in states 6 and7.

State Orientation1 Both markets not established2 ask1 > ask2 > bid2 > bid1

3 ask1 > ask2 > bid1 > bid2

4 ask2 > ask1 > bid2 > bid1

5 ask2 > ask1 > bid1 > bid2

6 ask1 > bid1 > ask2 > bid2

7 ask2 > bid2 > ask1 > bid1

8 Other (locked)

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Table 5: Summary of market states The table reports the percentage of time each marketis in a particular state as defined by Table 2.

State Ericsson Nokia SAS Stora Enso Telia Sonera Tieto1 4.2% 3.9% 6.7% 2.4% 1.3% 2.5%2 0.0% 42.4% 10.3% 54.4% 11.7% 55.8%3 1.2% 14.7% 27.2% 16.0% 29.2% 14.8%4 2.3% 15.7% 27.0% 19.2% 36.2% 18.4%5 87.3% 0.1% 16.5% 0.5% 13.6% 0.8%6 1.0% 10.5% 5.6% 3.8% 3.0% 3.0%7 3.9% 12.7% 6.8% 3.7% 5.0% 4.6%8 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

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Table 6: Average number of unique visits per day

State Ericsson Nokia Nordea SAS Stora Enso Telia Sonera Tieto1 108.58 1.03 1.02 1.97 1.03 1.02 1.032 0.11 1068.14 184.86 81.86 436.62 169.79 403.383 59.73 744.69 472.45 110.18 250.11 179.74 227.744 94.43 823.62 489.28 113.83 279.75 196.40 257.245 239.38 56.97 481.88 98.68 40.16 119.23 47.396 8.83 285.75 130.98 28.09 57.54 33.57 34.377 20.68 338.70 150.08 29.90 68.32 44.93 42.758 0.46 2.34 1.03 0.07 1.40 1.07 0.83

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Table 7: Average duration of visits to each state in seconds

State Ericsson Nokia Nordea SAS Stora Enso Telia Sonera Tieto1 101.34 164.75 124.91 408.15 61.39 183.26 160.502 20.04 5.84 14.49 81.26 18.22 48.58 17.943 124.46 11.94 15.11 48.89 33.90 27.06 37.694 86.00 11.71 14.15 46.21 31.26 26.94 37.075 9.41 4.39 14.80 47.98 13.10 49.39 20.306 52.04 8.16 23.85 114.40 34.62 74.75 47.767 34.73 7.20 20.48 110.84 34.23 70.51 46.908 49.04 9.51 13.37 46.29 38.13 35.05 37.24

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Table 8: Unique visits to each state

Total Unique VisitsState Ericsson Nordea Nokia SAS Stora Enso Telia Sonera Tieto

1 12704 119 120 231 121 119 1202 13 21629 124972 9578 51085 19865 471963 6988 55277 87129 12891 29263 21029 266464 11048 57246 96363 13318 32731 22979 300975 28008 56380 6665 11545 4699 13950 55456 1033 15325 33433 3286 6732 3928 40217 2420 17559 39628 3498 7994 5257 50028 54 121 274 8 164 125 97

Total 62268 223656 388584 54355 132789 87252 118724

Percentage BasisState Ericsson Nordea Nokia SAS Stora Enso Telia Sonera Tieto

1 20.40% 0.05% 0.03% 0.42% 0.09% 0.14% 0.10%2 0.02% 9.67% 32.16% 17.62% 38.47% 22.77% 39.75%3 11.22% 24.72% 22.42% 23.72% 22.04% 24.10% 22.44%4 17.74% 25.60% 24.80% 24.50% 24.65% 26.34% 25.35%5 44.98% 25.21% 1.72% 21.24% 3.54% 15.99% 4.67%6 1.66% 6.85% 8.60% 6.05% 5.07% 4.50% 3.39%7 3.89% 7.85% 10.20% 6.44% 6.02% 6.03% 4.21%8 0.09% 0.05% 0.07% 0.01% 0.12% 0.14% 0.08%

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Table 9: Size of arbitrage opportunities in State 6 This table reports the percentage oftime conditional on being in State 6 in which the size of the arbitrage opportunity fell intoa specifc range. The size of the arbitrage opportunity in State 6 is defined as the differencebetween bid1 and ask2 times the minimum of the depth available at those to prices.

Ericsson Nokia Nordea SAS Stora Enso Telia Sonera Tieto< 100 Euros 81.13% 82.14% 88.96% 94.00% 92.21% 89.36% 97.02%

100-200 Euros 7.99% 9.33% 6.89% 3.57% 4.10% 5.20% 2.98%200-300 Euros 5.94% 3.53% 2.18% 1.27% 1.62% 1.35% 0.00%300-400 Euros 1.72% 1.78% 0.96% 0.11% 0.62% 0.99% 0.00%400-500 Euros 2.34% 1.05% 0.33% 0.12% 0.72% 0.54% 0.00%500-600 Euros 0.62% 0.59% 0.25% 0.76% 0.42% 0.66% 0.00%600-700 Euros 0.14% 0.40% 0.13% 0.17% 0.31% 0.22% 0.00%700-800-Euros 0.08% 0.37% 0.12% 0.00% 0.00% 0.39% 0.00%900-1000 Euros 0.04% 0.20% 0.05% 0.00% 0.00% 0.31% 0.00%> 1000 Euros 0.01% 0.62% 0.14% 0.00% 0.00% 0.97% 0.00%

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Table 10: Size of arbitrage opportunities in State 7 This table reports the percentageof time conditional on being in State 7 in which the size of the arbitrage opportunity fell intoa specifc range. The size of the arbitrage opportunity in State 6 is defined as the differencebetween bid2 and ask1 times the minimum of the depth available at those to prices.

Ericsson Nokia Nordea SAS Stora Enso Telia Sonera Tieto< 100 Euros 95.77% 69.98% 88.73% 92.73% 92.26% 86.82% 94.51%

100-200 Euros 1.66% 14.36% 6.22% 4.60% 5.50% 7.25% 2.40%200-300 Euros 0.85% 6.19% 2.26% 1.71% 1.48% 2.81% 1.09%300-400 Euros 1.07% 3.23% 1.18% 0.52% 0.47% 1.18% 0.51%400-500 Euros 0.25% 1.91% 0.52% 0.04% 0.16% 0.87% 0.39%500-600 Euros 0.20% 1.12% 0.31% 0.15% 0.11% 0.63% 0.18%600-700 Euros 0.12% 0.72% 0.23% 0.12% 0.02% 0.25% 0.18%700-800-Euros 0.04% 0.45% 0.11% 0.04% 0.00% 0.13% 0.19%900-1000 Euros 0.03% 0.33% 0.12% 0.05% 0.00% 0.03% 0.05%> 1000 Euros 0.02% 1.71% 0.33% 0.05% 0.00% 0.05% 0.51%

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Table 11: Transition matricies (event-based)

Ericsson1 2 3 4 5 6 7 8

1 0.000 0.000 0.012 0.044 0.897 0.002 0.045 0.0002 0.000 0.000 0.615 0.308 0.000 0.000 0.077 0.0003 0.033 0.001 0.000 0.000 0.883 0.081 0.000 0.0014 0.060 0.000 0.000 0.000 0.822 0.000 0.116 0.0025 0.399 0.000 0.228 0.335 0.001 0.016 0.020 0.0016 0.039 0.000 0.409 0.000 0.551 0.000 0.000 0.0017 0.244 0.000 0.000 0.445 0.309 0.000 0.000 0.0028 0.056 0.000 0.093 0.333 0.352 0.037 0.130 0.000

Nokia1 2 3 4 5 6 7 8

1 0.000 0.294 0.176 0.143 0.017 0.202 0.168 0.0002 0.000 0.000 0.445 0.478 0.000 0.032 0.044 0.0013 0.000 0.619 0.000 0.007 0.037 0.335 0.000 0.0014 0.000 0.608 0.007 0.000 0.032 0.000 0.352 0.0015 0.000 0.003 0.484 0.477 0.000 0.020 0.017 0.0006 0.000 0.168 0.826 0.000 0.005 0.000 0.000 0.0017 0.000 0.169 0.000 0.827 0.003 0.000 0.000 0.0018 0.004 0.296 0.259 0.266 0.004 0.062 0.109 0.000

Nordea1 2 3 4 5 6 7 8

1 0.000 0.025 0.252 0.168 0.151 0.202 0.193 0.0082 0.000 0.000 0.483 0.490 0.003 0.010 0.013 0.0013 0.001 0.190 0.000 0.045 0.497 0.266 0.000 0.0014 0.000 0.182 0.044 0.000 0.479 0.000 0.295 0.0015 0.001 0.001 0.496 0.490 0.000 0.006 0.006 0.0006 0.001 0.021 0.932 0.000 0.044 0.000 0.000 0.0017 0.001 0.017 0.000 0.941 0.041 0.000 0.000 0.0008 0.000 0.107 0.289 0.248 0.198 0.124 0.033 0.000

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Table 12: Transition matricies (event-based)

SAS1 2 3 4 5 6 7 8

1 0.000 0.126 0.177 0.186 0.065 0.203 0.242 0.0002 0.003 0.000 0.455 0.478 0.002 0.032 0.030 0.0003 0.003 0.334 0.000 0.025 0.423 0.214 0.000 0.0004 0.004 0.332 0.025 0.000 0.415 0.000 0.225 0.0005 0.002 0.001 0.483 0.487 0.000 0.014 0.013 0.0006 0.013 0.117 0.785 0.002 0.079 0.003 0.000 0.0007 0.013 0.120 0.002 0.782 0.078 0.001 0.004 0.0008 0.000 0.000 0.375 0.250 0.125 0.125 0.125 0.000

Stora Enso1 2 3 4 5 6 7 8

1 0.000 0.380 0.157 0.157 0.025 0.124 0.157 0.0002 0.001 0.000 0.443 0.491 0.000 0.029 0.034 0.0013 0.000 0.748 0.000 0.001 0.073 0.176 0.000 0.0024 0.001 0.736 0.001 0.000 0.073 0.000 0.188 0.0015 0.000 0.002 0.471 0.499 0.000 0.014 0.012 0.0026 0.000 0.346 0.641 0.000 0.011 0.000 0.000 0.0017 0.000 0.333 0.000 0.655 0.010 0.000 0.000 0.0018 0.012 0.323 0.378 0.183 0.061 0.000 0.043 0.000

Telia Sonera1 2 3 4 5 6 7 8

1 0.000 0.076 0.261 0.261 0.092 0.160 0.151 0.0002 0.001 0.000 0.483 0.484 0.001 0.014 0.016 0.0013 0.002 0.458 0.000 0.050 0.316 0.171 0.000 0.0024 0.002 0.428 0.047 0.000 0.311 0.000 0.211 0.0015 0.002 0.001 0.471 0.520 0.000 0.002 0.003 0.0016 0.000 0.040 0.943 0.001 0.013 0.001 0.001 0.0027 0.001 0.038 0.001 0.947 0.012 0.000 0.002 0.0008 0.000 0.200 0.384 0.248 0.120 0.040 0.008 0.000

Tieto1 2 3 4 5 6 7 8

1 0.000 0.433 0.175 0.133 0.017 0.108 0.133 0.0002 0.002 0.001 0.451 0.506 0.000 0.018 0.023 0.0013 0.001 0.786 0.000 0.002 0.096 0.115 0.000 0.0014 0.001 0.781 0.001 0.000 0.089 0.000 0.128 0.0015 0.000 0.002 0.474 0.491 0.000 0.019 0.014 0.0006 0.001 0.300 0.662 0.000 0.035 0.000 0.000 0.0027 0.001 0.285 0.000 0.683 0.030 0.000 0.001 0.0008 0.000 0.454 0.175 0.278 0.021 0.062 0.010 0.000

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Table 13: Correlation Matrix for Mid-Quote Deviations

Nokia Nordea Stora Telia Tieto SEK/EUREnso Sonera

Nokia 1.000Nordea 0.177 1.000Stora Enso 0.061 0.075 1.000Telia Sonera 0.137 0.054 0.059 1.000Tieto 0.153 0.152 0.121 0.054 1.000SEK/EUR -0.283 -0.225 -0.103 -0.157 -.280 1.000

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Figure 1: Illustrations of State Definition

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Figure 2: SAS

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Figure 3: Telia Sonera

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Figure 4: Frequency distribution of deviations with a 10 euro resolution for Nokia.

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Figure 5: Frequency distribution of deviations with a 10 euro resolution for SAS.

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Figure 6: Frequency distribution of deviations with a 10 euro resolution for Telia Sonera.

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