Artificial Multi-Agent Stock Markets: Simple Strategies ...

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  • Good Afternoon, Ladies and Gentlemen and welcome to this presentation. My name is Arvid Hoffmann and I work at the University of Groningen in The Netherlands. Today’s presentation might be a little different than what you have expected. Then, as I was preparing this presentation I realized that I should not present the paper that is included in the proceedings. After all, at the last conference, I promised to develop a new simulation model of a stock market that would overcome the limitations of the one I presented then, back in 2005 in Lille. However, the paper in the proceedings is a last refinement made to this model, but does not adequately reflect the current state of my work. Therefore, today, unlike the program, I will not present about the paper as it is published in the proceedings of this conference. Rather, I will share with you a perspective on the social simulation of stock markets and present the artificial stock market SimStockExchange. I have recently developed this model which overcomes the limitations of the previously presented model and is more representative for my research program than the paper that is included in the proceedings.
  • Before diving into the details of this presentation, I would like to give an outline of this presentation: First, I will catch up memories with you by discussing what it exactly was that my research program aimed to achieve. Then, I will shortly refresh your memory by repeating the summary of limitations of the previous work and the promise I made last year to overcome these limitations. After this trip down memory lane, I will briefly discuss some theoretical issues. Then, I will outline the steps that I have already taken and will take in building the new artificial stock market, and introduce the model. A short model demonstration will follow to give an impression of SimStockExchange. After this brief demo, I will outline two preliminary simulation experiments. Then off course, it is again time to discuss what we have and have not yet achieved and outline the perspective for future research. Finally, there is time for your questions and comments.
  • These first few slides are the same as last year and are intended to fresh up the memory of the participants who where at this conference last year and serve as an introduction to my work for the newcomers.
  • Many agent-based computational models in finance have been developed and presented in top journals over the last few years. However, almost all of these models spring from the modern finance conception. Also, a large part of these models has been developed from an interacting agents perspective, in which fundamentalist agents are let to interact with chartist or trend following agents and the resulting market dynamics are analyzed. However, the literature on the application of agent-based models in behavioral finance is very limited. Agent based models in behavioral finance in which the agents have empirically estimated trading and interaction rules are practically not heard of. But if you do know of more models in that field, I will happily accept any reference you have to such a model. The above makes the objective of my research program easy: develop and build an empirically validated agent-based artificial stock market build on behavioral finance principles.
  • In our empirical study, we have performed a survey amongst individual investors in The Netherlands. This study focused on the effect of different needs (amongst which more socially oriented needs) and their amount of investment related knowledge and experience on their social conformity behavior. It was found that investors with less investment related knowledge and experience, and who therefore perceived a higher level of risk, performed more informative and normative conformity behavior. In the next step, we will discuss how we have used this empirical micro level data in building an artificial stock market.
  • Although one could argue that conventional mathematical theorizing is also capable of investigating the macro level effects of micro level rules, agent based computational modeling is a better match for our research problem for a number of reasons: Easy to limit agents’ rationality Facilitates the study of the effects of heterogeneity in the agent population Generates a dynamical history of the process under study Interaction of agents in social networks is facilitated In other words, the SimStockExchange was born
  • Selecting a more appropriate empirical benchmark can be necessary when the empirical time horizon (daily, weekly, monthly) and the time horizon implied by the simulation model are incompatible. The above is an iterative process.
  • Following these steps, we have developed the artificial stock market SimStockExchange Different social network structures, like the small world, scale free of regular torus network, differ in their information diffusion capacities and are therefore expected to influence the market dynamics of the model.
  • At every start of a simulation experiment, the SSE requires the user to make a choice amongst a number of settings. First are the more general settings, like which network one wants to use, whether bankrupt agents should be replaced by new agents, and the type of graphical outputs one desires. Second, the SimStockExchange prompts the user to insert a random seed. One can either reuse an existing seed, or accept the random seed the computer has just generated. The reusing of an existing seed offers the user the possibility of using exactly the same social network formalization in a number of different simulation experiments. In this way, one can be sure, that different results are not caused by changes in the positions of agents in the network. Then, one has to make a choice for the news generation process. One can either choose for a uniform distribution of noise with a certain bandwidth around the current price or for a normal distribution with a mean equal to the current price and a set standard deviation. After one has entered all these information, one can formalize the agents. There are three possible ways to do this: One can set the parameters individually for each agent, One can set the parameters for a group of agents either as a fixed setting for every agent or as a distribution (uniform or normal), One can load an agent file, for example a CSV file with empirically derived parameter settings for each individual agent. Then, one can start the simulation run. Immediately after the simulation run is started, a new folder, named logs, is created in the same folder as where the executable file version of the SSE has been saved. In this folder, a number of text files are written. In these text files, the agent parameter settings and the stock price and return time series are saved. the SimStockExchange program prompts for a random seed. One can either accept the random seed that the computer and generates, or a reuse an existing random seats, so one can use exactly the same network as in another simulation experiments. Then, one has to choose amongst a number of settings, e.g., which network one wants to use, which outputs one desirous
  • A torus network is simply a lattice whose edges are connected, and a scale free network is a network in which the distribution of the connectivity of the nodes of the network follows a power law, i.e. there are many nodes with only a few connections to others, and there are only a few nodes with many connections to others. Many networks in real life, like those of web pages on the Internet and scientific citations, behave like a scale free network and also have small world characteristics. Due to the superior information diffusion characteristics of the scale free network, we expect random shocks (news in the form of random noise) to dampen out quickly in these networks. Therefore, these networks are expected to display less volatility clustering than networks with poorer information diffusion characteristics, like the regular torus network.
  • I will not go into detail about all these parameter settings but would just like to stress, that the settings of the agent’s confidence and their trading strategies are taken from our first empirical study. After deletion of incomplete questionnaires, this resulted in 167 investors, therefore this number of investor agents in the model.
  • This overview of the results of the two simulation experiments and the comparison with the two empirical stock markets show that the price and return dynamics of SimStockExchange have a number of strong qualitative resemblances with those observed in real markets. The SimStockExchange is able to reproduce a number of stylized financial market facts like a very small autocorrelation in the asset returns distribution as indicated by the Durbin Watson statistic. Also, the simulation results show volatility clustering as indicated by the GARCH analysis. However, due to the fact that these two experiments were only preliminary simulation runs, the quantitative resemblance of the results is limited. The first row shows the standard deviation of the returns, i.e. the market volatility, for the two simulation experiments as well as for the two empirical stock markets. The parameters for the news were chosen so that in both cases the expected value of the standard deviation was 0.02, comparable to the values that can be observed in the AEX and DJI, as depicted in the two right-most columns of the first row. Both experiments show a higher variability than was theoretically and empirically expected, and the difference in the standard deviation between the cases is minimal. Social interaction amongst investors in the SSE is a possible reason for this increased level of the variability. Investors partly reacting on news and partly reacting on each other might create self-reinforcing dynamics, thereby pushing the standard deviation of returns to higher levels. The second row shows the kurtosis or degree of peakedness of a distribution of the simulation experiments as well as that of the two empirical stock markets. The two simulation experiments show a kurtosis that approximates that of a normal distribution - which has a kurtosis of 3.00 - while the two empirical stock markets show a significant amount of excess kurtosis. The latter are leptokurtotic; a pattern that is common for real asset returns distributions. Using the parameter settings from table 2, the SSE does not replicate this empirically found fact. This can be explained from the fact, that the news generation process in the SSE currently is also based on a normal distribution, while the underlying dynamics of the news generation process in real markets is undefined by nature. The third row shows the Durbin Watson statistic, testing for autocorrelation in the residuals. [1] We can observe from table 3, that the two simulation experiments take on test values around 2.00, which lines up well both qualitatively and quantitatively with the test values found in the empirical stock markets. The two simulation experiments display a very small amount of negative autocorrelation, while the same type of autocorrelation occurs in the real stock markets, but with an even smaller effect size. The next three rows show a common test for volatility persistence or "volatility clustering" in finance, called the (Generalized) ARCH test. [2] A typical pattern observed for real asset returns is that the coefficients on all three terms in the conditional variance equation are highly statistical significant, with a small value for the variance intercept term C, a somewhat larger ARCH (squared errors (yesterday’s volatility))term, and an even larger GARCH (conditional variance (yesterday’s fitted/estimate variance))term. The ARCH term represents the lagged squared error, while the GARCH term represents the lagged conditional variance. For real asset returns, both terms summed together are generally found to be close to unity. This indicates that shocks to the conditional variance will be highly persistent, i.e. there is volatility persistence. The results of both simulation experiments line up well qualitatively with the empirical stock markets with regard to the relative proportions of the three terms of the conditional variance equation. Only in the first experiment, however, we observe a statistically significant GARCH term that also lines up well quantitatively with the terms found in the real asset returns of the AEX and the DJI. For experiment 2, with the scale free network, none of the terms in the conditional variance equation is statistically significant, while experiment 1, with a regular torus network, displays a highly significant GARCH effect. So, for these two experiments, we observe ceteris paribus that in artificial stock markets with scale free networks, there is no statistically significant proof of volatility clustering, but artificial stock markets with a torus network display volatility clustering. A possible explanation for this is that the superior information diffusion capacities of the scale free network facilitate an immediate absorption of the news by all network members and inhibit news shocks of yesterday to have much effect on today’s returns. Moreover, one could argue that in spite of today’s ubiquitous information through e.g., mass medial devices and the Internet, which have lowered the cost of information drastically, and despite the fact that theoretically and empirically there is a good case for the society as a scale free network, in reality (at least for the investing population of society) the society is more likely to behave like a torus network with regard to the information diffusion capacities, where information sometimes takes long to travel to remote corners of the network and shocks of the past continue to influence the present for a considerable period of time. [3] [1] Autocorrelation is the correlation of a process Xt against a time-shifted version of itself. The efficient markets hypothesis of modern finance literature assumes that the residuals of today are uncorrelated with the residuals of tomorrow. That is, today’s news is completely and immediately absorbed in today’s stock prices and has no effect on tomorrow’s stock prices. When the Durbin Watson statistic takes on the test value of two, this corresponds to the case where there is no autocorrelation in the residuals. When this statistic takes on a test value of zero, this corresponds to the case of perfect positive autocorrelation in the residuals. In case the test statistic takes on the value of four, this corresponds to the case where there is perfect negative autocorrelation in the residuals. [2] ARCH is the test for conditional heteroscedasticity as developed by Engle (1982). GARCH is a generalized model for conditional heteroscedasticity as developed independently by Bollerslev (1986) and Taylor (1986). [3] However, these results are achieved with a news generation process that is remote from the news arrival processes in reality. As indicated before, in real markets, the news generation process if undefined by nature. Scale free networks might actually approximate reality closer with regard to the stylized financial market facts in case real news is driving the markets instead of normally distributed noise.
  • The SSE, remains an estimation of real stock markets. In a real stock market, days go by on which no newsworthy events appear to happen. On another day, the executive board of a large company admits that there was accounting fraud or a transaction was wrongfully booked under “goodwill”. On yet another day, investors panic without any apparent reason. These are all examples of extreme events, of which it is impossible to formalize them all in a single artificial stock market in the form of specific agent or more general model rules. Even when one would succeed in including them all in an artificial market, this would make the results of this market (1) analytically intractable, and (2) merely a mirror of the past instead of a useful environment in which to test specific hypotheses. Artificial stock markets can be used to explore how different micro level behavioral processes aggregate to macro level phenomena and, in turn, how these aggregated outcomes affect individual stock traders' behavior. This would contribute to understanding the dynamics behind the stock market events as discussed.
  • I hope that this presentation was interesting and useful to you and will do my best to answer your questions.
  • Artificial Multi-Agent Stock Markets: Simple Strategies ...

    1. 1. SimStockExchange Building a more Realistic Artificial Stock Market Arvid O.I. Hoffmann © 2006
    2. 2. Outline of this presentation <ul><li>Research Objectives and Methods </li></ul><ul><li>Last Year’s Limitations </li></ul><ul><li>Last Year’s Promise </li></ul><ul><li>Theoretical Introduction on Agent-Based Computational Finance </li></ul><ul><li>Four Steps in Building Empirically More Realistic Artificial Stock Markets </li></ul><ul><li>An Introduction to the SimStockExchange Artificial Stock Market </li></ul><ul><li>Introductory Software Demonstration </li></ul><ul><li>Two Preliminary Simulation Experiments </li></ul><ul><li>What have we achieved by now? </li></ul><ul><li>What have we not achieved by now? </li></ul><ul><li>What will we do next? </li></ul><ul><li>Questions? </li></ul>
    3. 3. Research Objectives and Methods <ul><li>What do we want? </li></ul><ul><ul><li>A better understanding of micro level investor behavior </li></ul></ul><ul><ul><li>A better understanding of macro level stock market dynamics </li></ul></ul><ul><ul><li>A better understanding of the micro-macro link </li></ul></ul><ul><li>What methods will we use? </li></ul><ul><ul><li>Consumer and Investment research theories </li></ul></ul><ul><ul><li>Survey research amongst individual investors </li></ul></ul><ul><ul><li>Combine these theories and survey data to build and parameterize a multi-agent simulation model </li></ul></ul><ul><ul><li>Compare outcomes simulation with real market data </li></ul></ul>
    4. 4. Last Year’s Limitations <ul><li>Investors in last year’s model did not get information from their social network, but only derived it directly from stock prices </li></ul><ul><li>New information arrival to the market was not incorporated </li></ul><ul><li>Effect of different social networks on information diffusion processes was not studied </li></ul><ul><li>Market dynamics were generated by the actions of investors, but the cognition of investors was never affected by the evolution of the market; there was no feedback mechanism </li></ul><ul><li>Investors could only trade the shares of one company </li></ul><ul><li>Investors were not limited by a budget </li></ul>
    5. 5. <ul><li>Build a new multi-agent simulation model with the following properties: </li></ul><ul><ul><li>Implementation of different social network structures </li></ul></ul><ul><ul><li>Feed news into the market about the expectation of next period’s stock price </li></ul></ul><ul><ul><li>An agent’s success in the market feeds back into his choice between different investment strategies </li></ul></ul><ul><ul><li>Agents have a personal budget </li></ul></ul><ul><ul><li>Agents can choose between different shares and/or cash </li></ul></ul><ul><li>This resulted in the SimStockExchange Artificial Stock Market </li></ul>Last Year’s Promise
    6. 6. Theoretical Introduction <ul><li>Many models have been developed in Agent-Based Computational Finance (LeBaron, 2000). </li></ul><ul><li>These models help to explain stylized financial market facts that are hard to explain using traditional representative agent perspectives (LeBaron, 1999). </li></ul><ul><li>However, almost all of these models spring from modern finance: models based on behavioral finance (BF) theories are rare. Takahashi and Terano (2003) is an early BF paper. </li></ul><ul><li>Even less models use empirical data to validate their agent’s trading and interaction rules and evaluate the macro results. </li></ul>
    7. 7. Building empirically more realistic artificial stock markets: Step 1 <ul><li>In general: use multi-disciplinary theory to formulate specific hypotheses with regard to the individuals or institutions central to the study and test these hypotheses using empirical data. </li></ul><ul><li>In our case: </li></ul><ul><ul><li>Perform empirical study on investor behavior (micro level), </li></ul></ul><ul><ul><li>Perform statistical analyses on stock market data (macro level). </li></ul></ul><ul><li>We focus on investors’ (social) risk reducing strategies and stylized financial market facts like volatility clustering and fat tails of asset returns distributions. </li></ul>
    8. 8. Building empirically more realistic artificial stock markets: Step 2 <ul><li>Discover the effect of (social) interactions amongst micro level subjects on macro level institutions. </li></ul><ul><li>In our case: </li></ul><ul><li>Investigating the effect of interactions amongst micro level investors on macro level stock market dynamics. </li></ul><ul><li>An artificial stock market is created with empirically validated trading and interaction rules. </li></ul>
    9. 9. Building empirically more realistic artificial stock markets: Step 3 <ul><ul><li>Estimate the empirical plausibility of the macro level stock market price and returns data. </li></ul></ul><ul><ul><li>More specific: compare macro level simulation data with empirically found macro level data. </li></ul></ul><ul><ul><li>In our case: </li></ul></ul><ul><ul><li>Compare e.g., the occurrence of stylized financial market facts in the price and returns time series of the simulation model with those of a representative empirical stock market. </li></ul></ul>
    10. 10. Building empirically more realistic artificial stock markets: Step 4 <ul><li>Successful execution of step 1-3 results in quantitative and qualitative agreement between the model and reality on both a micro and a macro level. </li></ul><ul><li>However, often a (partial) mismatch between the simulation generated data and the empirical data remains and/or not every model component could be empirically validated. </li></ul><ul><li>To reduce this mismatch, reconsider the first three steps: </li></ul><ul><ul><li>Perform more empirical research, </li></ul></ul><ul><ul><li>Modify existing agent rules or create new ones, </li></ul></ul><ul><ul><li>Select a more appropriate empirical benchmark. </li></ul></ul>
    11. 11. Introducing: SimStockExchange (SSE) <ul><li>The SSE artificial stock market features different types of investors who conduct transactions based on the investment rules as formalized for each type. </li></ul><ul><li>At the start of each simulation run, investor agents are allocated a number of stocks in their portfolio and an amount of cash. </li></ul><ul><li>Agents can decide to invest all or part of their budget in a number of different stocks or to keep all or part of their budget in cash. </li></ul><ul><li>Different social networks can be formalized in which the agents are positioned and in which market interactions take place. </li></ul>
    12. 12. Introducing: SimStockExchange (SSE) <ul><li>The SSE operates in 4 steps, of which the last one is optional: </li></ul><ul><li>Every investor in the market receives a personal signal (information on the next period’s expected price) and observes the current market price. </li></ul><ul><li>Depending on the confidence of the investor, the personal signal is weighted to a greater or lesser extent with the signal that neighboring agents have received or the other investor’s behavior is simply copied. Based on this an order is forwarded to the stock market. </li></ul><ul><li>A new market price is calculated based on the crossing of orders in the order book. </li></ul><ul><li>The agent’s rules can be updated according to their results: more successful agents become more confident. </li></ul>
    13. 13. A small software demonstration… Start SimStockExchange Random seed: 1147092813406
    14. 14. General outline simulation experiments <ul><li>We studied the time series behavior of the simulated return time series in two different network situations: </li></ul><ul><ul><li>Regular torus network </li></ul></ul><ul><ul><li>Barabasi and Albert scale free network </li></ul></ul><ul><li>We have used empirically obtained settings for an investors’ level of confidence and their risk reducing investment strategies. </li></ul><ul><li>The market was run for 10,000 time steps. </li></ul>
    15. 15. Simulation experiments: parameters <ul><li>The following parameter settings were used: </li></ul>
    16. 16. Simulation experiments: statistics
    17. 17. What have we achieved by now? <ul><ul><li>We have built the SSE, which is a practical example of combining empirical micro and macro level data, theoretical micro and macro level perspectives, and a multi-agent based social simulation approach when building artificial stock markets. </li></ul></ul><ul><ul><li>The SSE shows a number of strong qualitative and quantitative resemblances with real market data. </li></ul></ul><ul><ul><li>This makes the SSE a valid and valuable platform for investigating micro-macro links in stock markets. </li></ul></ul>
    18. 18. <ul><li>Limitations of the SSE on both a micro and a macro level are: </li></ul><ul><ul><li>With regard to the micro level agent rules and news process, the SSE is a model, and therefore a simplified image of real stock markets. </li></ul></ul><ul><ul><li>Strong qualitative resemblances with real markets makes it a fruitful avenue for future research, but quantitatively, there is room for improvement. </li></ul></ul>What have we not yet achieved by now?
    19. 19. What will we do next? <ul><li>We will further improve the model: </li></ul><ul><ul><li>Use empirical data to formalize the social network. </li></ul></ul><ul><ul><li>Compare the time horizons of the simulation model with the real world. </li></ul></ul><ul><ul><li>Include a trend in the news akin to that in real stock markets. </li></ul></ul>
    20. 20. Questions? Visit www.simstockexchange.com or www.arvidhoffmann.nl for a free model download, more information and papers.
    21. 21. Torus Network

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