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01-08-2014 | Research Article

The determinants of a cross market arbitrage opportunity: theory and evidence for the European bond market

Authors: Marcelo Perlin, Alfonso Dufour, Chris Brooks

Published in: Annals of Finance | Issue 3/2014

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Abstract

This paper examines the determinants of cross-platform arbitrage profits. We develop a structural model that enables us to decompose the likelihood of an arbitrage opportunity into three distinct factors: the fixed cost to trade the opportunity, the level at which one of the platforms delays a price update and the impact of the order flow on the quoted prices (inventory and asymmetric information effects). We then investigate the predictions from the theoretical model for the European Bond market with the estimation of a probit model. Our main finding is that the results found in the empirical part corroborate strongly the predictions from the structural model. The event of a cross market arbitrage opportunity has a certain degree of predictability where an optimal ex ante scenario is represented by a low level of spreads on both platforms, a time of the day close to the end of trading hours and a high volume of trade.

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For instance, see p. 373 of Harris (2003) and the first paragraph of Roll et al. (2007).

See, for example,Malkiel (2003).

See, for example, Hull (2002).

See Abreu and Brunnermeier (2002).

This is different from noise trader risk as it does not necessarily originate from traders with erroneous beliefs, but also from the time that other arbitrage trader will step into the market to correct the mispricing.

There is a clear example of such a risk in financial history—namely the LTCM episode. See Lowenstein (2002) for details.

See Hasbrouck (1996) for details.

For more information regarding properties of a random walk model, see Hasbrouck (2007).

This variable is also usually defined as a Gaussian white noise.

The positivity of the parameters is the result of the expected stylized effects in microstructure theory such as the inventory problem.

Some remarks should be made with respect to the process underlying the order flow. In general, it would be more realistic to assume that order flow has a mean reverting component of the type \(-\alpha \left( {q_{t-1} -m_{t-1} } \right) \), where \(\alpha \) is the reaction of traders to the mispricing of the asset. But ignoring such a mean reverting effects does not change the main point of this derivation, which is to show that arbitrage opportunities are the result of microstructure frictions. Given that, we choose to keep the simpler case with an exogenous process for order flow, which makes the following derivations far more tractable.

This parameter is bounded by zero and one.

This is not exactly evident from (2), but by substituting \(m_t\) for \(q_t\), it becomes clear that the trades will impact the quotes on a contemporaneous basis.

Aside, we could also have set the processes for quotes as \(q_{1,t} =m_{t-j} -b_1 I_{1,t-1} \) and \(q_{2,t} =m_{t-j-k} -b_2 I_{2,t-1} \) and it would not have change the results from the derivations. The effect which drives the result is the relative lag from one platform to the other, which in this case is measured by \(k\).

See p.97 in Hasbrouck (2007).

We assume that each trade is certain to be executed. This is different to the setup given in Kozhan and Tham (2009), in which the execution of arbitrage trades is uncertain. Further research could be taken in this direction, but we begin with a simpler scenario.

See the “Appendix 1” for a derivation.

See Maddala (1991) for further details on probit models.

Special thanks to James Le Sague for providing a resourceful econometric toolbox for Matlab (http://www.spatial-econometrics.com/).

For the cases where there are no events prior to the negative spread occurrence, we use the values of the variables in the previous 10 min interval.

We also run the probit models using the absolute value of order flow imbalance between platforms as one of the explanatory variables. The results are comparable to the use of the number of trades.

These are proposals for trading odd lots.

MTS stands for “MercatodeiTitoli de Stato”. See http://www.mtsmarkets.com/ for more details.

The identity of the counterparties, however, is revealed after the trade for clearing and settlement purposes. This anonymous system was implemented in 1997. Before this time, the market maker’s identity was visible by all participants.

See MTS (2007).

The ISIN code is a unique international identifier for each bond. Those codes are assigned by each country’s numbering agency.

These are bonds that cannot be redeemed prior to maturity.

This is based on the pricing function of a bond. The longer the maturity of the bond, the higher the sensitivity of the pricing function with respect to the discount rate. See Martellini et al. (2003) for details.

On average, the filtering removed 66 % of the original dataset. This means that, for the respective dataset, 34 % of the recorded events happened at the second and third levels of the order book.

The bond in question is clearly an outlier. Further inspection of the data shows a very high number of consecutive negative spreads when compared to the rest of the dataset. A reasonable explanation would be an operational problem with the time of the recording of prices on both platforms. Therefore, the arbitrage opportunities are probably overstated. The results for this particular case should be viewed with suspicion.

“Algorithm quoting” is the use of computers for controlling dealers’ quotes in the market. In this particular case, it represents a control from the software side which makes sure that no inter-platform arbitrage opportunity is created. But note that the software control is ex post reactive, meaning that it only becomes active after the arbitrage event occurred. The argument is that if it was ex ante reactive, no arbitrage opportunity would be found in the data.

Empirical evidence of this inventory management strategy can be found in Hasbrouck (2007).

This relation will be dependent on the requirements for disposing of inventory. Following our argument, we assume that the cost of disposing of inventory is lower than the required compensation for the overnight inventory risk.

The number of correct predictions is simply the number of times that the model correctly forecasts an arbitrage opportunity. We use a threshold of 50 % in such calculations. Similar calculations are conducted for the value in the column “Incorrect signals percentage,” but in this case, focus is on the number of incorrect signals generated by the model.

The tractability of the Gaussian density greatly simplifies the analysis.

Formally, the property is that if \(X\) and \(Y\) follow normals, then \(X+Y \) will also be normal with variance given by \(\sigma _{X+Y}^2 =\sigma _X^2 +\sigma _Y^2 +2\sigma _{X,Y} \).

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Akram, F., Rime, D., Sarno, L.: Arbitrage in the foreign exchange market: turning on the microscope. J Int Econ 76, 237–253 (2008)

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Title: The determinants of a cross market arbitrage opportunity: theory and evidence for the European bond market
Authors: Marcelo Perlin
Alfonso Dufour
Chris Brooks
Publication date: 01-08-2014
Publisher: Springer Berlin Heidelberg
Published in: Annals of Finance / Issue 3/2014
Print ISSN: 1614-2446
Electronic ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-013-0242-5

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