Arbitrage in Finance Markets

Arbitrage is the possibility to make riskless profit. The standard example is the trading of one financial instrument at different exchanges. In the case of a difference in the prices, we can buy the instrument at the exchange with the lower price and sell it at another exchange for the higher price. By doing this, we have made the difference of the prices as profit without any risk. Unfortunately, these possibilities do not exist very long because the principle of supply and demand balances out the price difference very fast. Furthermore, we have to consider the transaction costs. Therefore, we must be able to notice arbitrage opportunities very fast and to give the appropriate hint to the trader.
The examination of different arbitrage modells and the development of appropriate software is the goal of the project "High Performance Arbitrage Detection and Trading (HAT)". Together with other european partners from banking and software circles, we work on this ESPRIT-project. The partners are the Banque National de Paris (London), the London Business School, the companies Intrasoft (Athen) and Parsytec (Aachen) and Dresdner Bank among others.
The Reuters AG must be mentioned as a coordination partner, which gives the project partners the possibility to access their online information system. This is necessary, because the investigation needs online exchange data and the arbitrage opportunities will be delivered over the Reuters-net to the traders.

We have developed and examined 11 arbitrage modells. We distinguish between absolutely risk-free models, statistical and modell-based classes. Only the risk-free modells can be called "arbitrage opportunities". These modells contain, for example, the currency triangle, i.e. in case of appropriate price differences of the exchange rates, we can make profit by changing DEM in Yen, the Yen in US dollar and finally US dollar again in DEM.The other modells in this class make use of the Put-Call Parity, the Cheapest - to - Deliver - Arbitrage, the Covered - Interest - Rate - Arbitrage and the Equity - Index - Spot - Future - Arbitrage.
In the other two modell classes, we can make loss. However, we aim at constructing modells for the trade to be profitable with a high probability. Within the statistical arbitrage, we try to imitate the price of a target asset by a basket of other instruments. The construction of the basket is based on cointegration and principal component analysis.
If we observe a difference between the price of the basket and the price of the target asset, we do a trade. The sign of the mispricing between the target and the basket influences the way we trade, i.e. whether we buy the target and sell the basket or vice versa. The London Business School developed different trading strategies to incorporate the absolute value of the mispricing. The class of the modell-based arbitrage opportunities is comparable to the statistical modells. However, we try to forecast the price of a target asset by using a basket of other assets and their former prices. This means that only the target asset is traded, depending on the forecast.The forecast is determined by linear regression, neural networks or adaptive linear models (Kalman filter).
The aim in modelling was to transfer the ideas in concrete instances in the European stock and bond markets and to examine their profitability with statistical methods. Additionally, we must take into account the already mentioned transaction costs and so-called "slippage effects".
The main thing is to determine the risk to make loss instead of profit. Within the risk-free modells, a loss can occur by the slippage effect, because the trader needs more time to do the trade than the arbitrage opportunity exists. The other two model classes inherently have the possibility to make a loss. The London Business School developed different instances for the different classes. Our work was to test and examine these modells with respect to different criteria, as for example the Sharpe-Ratio, the variance of the returns or the semi-variance of the returns.

For using the arbitrage opportunities, a hard and software system was and still is being developed , to read in the online exchange data from Reuters and publish the data of so-called HATRICs on the Reuters net. This data can be seen only by authorized persons