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A Comparison of Different Trading Protocols in an Agent-Based Market

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A Comparison of Different Trading Protocols in an Agent-Based Market A comparison of different trading protocols in an agent-based market Paolo Pellizzari1,2 and Arianna Dal Forno1∗ Dept. of Applied Mathematics SSAV “Ca’ Foscari” University School of Adv. Studies in Venice Dorsoduro 3825/E Dorsoduro 3488/U Rio Novo 30123 Venice, Italy. 30123 Venice, Italy Previous draft: March 2005. This draft: November 2-nd 2005 Abstract We compare price dynamics of different market protocols (batch auction, continuous double auction and dealership) in an agent-based artificial exchange. In order to distinguish the effects of market archi- tectures alone, we use a controlled environment where allocative and informational issues are neglected and agents do not optimize or learn. Hence, we rule out the possibility that the behaviour of traders drives the price dynamics. Aiming to compare price stability and execution quality in broad sense, we analyze standard deviation, excess kurtosis, tail exponent of returns, volume, perceived gain by traders and bid-ask spread. Overall, a dealership market appears to be the best candidate in this respect, generating low volume and volatility, virtually no excess kurtosis and high perceived gain. 1 Introduction The observation that stock exchanges are run under a diverse set of market architectures and protocols raises some obvious and yet intriguing ques- tions. If we do not content ourself with the explanation that this is due to historic accidents or mere temporal and casual path-dependence, then we could investigate reasons explaining why exchanges developed so differ- ently and which are the main differences in the dynamic properties of the prevailing price or return time-series. ∗ Corresponding author: [email protected]. We thank the participants to seminars at the City University of London, Venice, Palermo for useful discussion. Marco LiCalzi is gratefully aknowledged, all the remaining mistakes are sadly ours. This work is partially supported by MURST, grant “Agent-based models of trading mechanisms and efficiency of informational dissemination” 1 We propose a terse model where allocative and informational effects are ruled out in order to be able to ascertain what is causing what, focusing on the price dynamics statistics. The use of agent-based methodology is particularly suited to control for unwanted side-effects that can otherwise blur the results. We develop an artificial market where simple agents trade a risky asset using different market protocols. As they receive no information, have no learning capability and act in a strictly controlled framework1, we hope to ascribe unambiguously the effects on price dynamics to the market protocol, which fundamentally is a blind mechanism to translate the demand of traders into actual orders and transactions. Even in the absence of price- discovery considerations or allocative efficiency remarks, this attribution might be of great interest to regulatory agencies or other policy makers in charge to devise and enforce trading rules. Some important measures of execution quality and price stability can be investigated in this framework, as suggested in [Madhavan, 2000] and [Audet et al., 2001]: execution quality can be assessed by quantification of volume, bid-ask spread, liquidity, volatility, fatness of tails of returns dis- tribution, kurtosis, market depth to mention some. Quite often, to borrow Madhavan’s words, we would expect from a market some key functions, namely good “provision of liquidity, continuity and price stabilization”. Al- though the overall execution quality of a market is a multidimensional con- cept, “price stability” in broad sense encompasses a wide set of previously mentioned measures and is quite often a targeted objective of regulators. Ex- cess volatility, kurtosis and tail exponents can be related to relevant financial shocks and to the emergence of bubbles in equity price. The burst of a price bubbles can adversely affect the economy and is sometimes deemed respon- sible of a recession, see [Bernanke and Gertler, 1999]. Institutions should be concerned about price volatility to limit financial fragility of banks and insur- ance firms whose risk exposure is dependent on price level and volatility, see [Vila, 2000]. Broad stability of markets could also enhance price-discovery and news interpretation as signals can be perceived more easily when the background noise (i.e. the volatility intrinsically generated by the trading protocol) is low. Different markets could serve to provide different performances with re- gard to the previously referenced criteria but a comprehensive comparison of different market protocols is, to the best of our knowledge, still lacking in the literature. There are obvious difficulties in comparing markets or in- stitutions in that it’s virtually impossible to “repeat” the experiment under different circumstances, as it is often the case in social sciences. If a sequence of trades tooks place in some market at some time because of some order 1This setting is suited to describe a calm period in the market, with little informational and liquidity flows and no tensions to be resolved (mergings, IPOs. ). Hence the results that we discuss in the sequel might be different from the ones generated in the presence of events like, say, September 11th. 2 flow, there is no hope to rewind the film changing the market protocol to see how different the outcomes would had been. Clever ideas have been used to overcome these design problems, see [Amihud and Mendelson, 1987] and [Amihud and Mendelson, 1991], using real exchanges data but some of their conclusions can be questioned in several ways. The effects of one specific market protocol are rather indirectly inferred in [Maslov, 2000] and [LiCalzi and Pellizzari, 2003] where simple agents (no information flows, adaptation or herding) interact in a Continuous Double Auction (CDA). Though there is no comparison among different markets, their argument is the following: the behavioral characteristics of the agents are so simple and innocuous that the resulting returns properties can chiefly be attributed to the mechanism that forms the price. While, there is an ap- preciable effort to stress the notion that dynamics features of the price time- series could be related to institutional devices rather than to the behaviour of agents, as is most often done in the literature (see [Day and Huang, 1900] or [Lux and Marchesi, 1999] 2), it is clear that their tentative conclusion needs much corroboration. In [LiCalzi and Pellizzari, 2005] different protocols are compared in their ability to converge to the unique allocative equilibrium. A good deal of experimental economics papers (see [Smith, 1988]) have faced the comparison of market protocols directly running real experiments with human subjects. These works often study small scale markets, that can be reproduced in vitro more easily and with reasonable costs. Being the result of real experiments, this body of work is largely immune to the previous mentioned “repeatability” criticisms. Some of the results might be not easily generalized to large-scale financial markets but we feel that other drawbacks could be pointed out. As noted elsewhere, experiments with real subjects might be subtly affected by the skill of the agents, the way in which they have been instructed or their understanding of the problem. Addition- ally and more importantly for our purposes, many experiments show that the agents learn quite rapidly and naturally to more and more effectively cope with their task. Again, the reported results might not be imputed to the market mechanism alone if agents are adapting and learning in time. These considerations should increase the appeal of running computational experiments to sketch some hopefully clear-cut comparisons among markets, by means of an artificial and controllable agent-based environment. The work in [Audet et al., 2001], [Bottazzi et al., 2005] and [Cliff, 2003] on the contrary, provide direct and explicit comparison of different market institutions. In the first paper, quite sophisticated retail agents are com- pared on two different market platforms, namely a dealership and a limit 2However, an early paper suggesting to investigate the effects of different protocols is [LeBaron, 2001]: “This can be both a curse and a blessing to market designers. On the bad side it opens up another poorly understood set of design questions. However, it may have the beneficial effect of allowing one to study the impact of different trading mechanisms”. 3 order market3. The findings by Audet and coauthors are rich and depend both on the features of the learning agents and the dealers, their risk aver- sion, heterogeneity and number (that is a proxy of market depth). If the utility of the final welfare is used to assess the quality, then the dealership market would be preferred in thin environments or by investors affected by large liquidity shocks, for example. [Cliff, 2003] offers a novel way to compare different markets. A contin- uous space of auctions, including as special cases the usual double auction, the English and the Dutch auctions, is explored in order to minimize Smith’s α dispersion index by a genetic algorithm. The fresh idea is that agents, equipped with some sort of machine learning capabilities, coevolve optimiz- ing their own profit together with the auction. Hence, the procedure really finds at the same time the best type of agents suited for the most efficient market structure. This is interesting as it can be argued that agents would most probably react to different institutional architectures changing their behaviour for self-interested purposes. As far as we know, no other papers investigate the mutual adaptation of traders and market mechanisms. The paper by [Bottazzi et al., 2005] is a careful comparison of three al- ternative architectures and follows a line similar to our approach. In their model, myopic, quadratic utility maximizing agents trade in different set- ups, namely a Walrasian auction, a batch auction and a ‘order-book’ mech- anism. Ecologies of agents are shaped by the fraction of chartist traders, extrapolating the future from past returns, that coexists with the remain- ing part of purely noisy investors.
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