Presentation on theme: "Market Mechanism Analysis Using Minority Game Market Models"— Presentation transcript:
1 Market Mechanism Analysis Using Minority Game Market Models Y. Chen, T. Kohashi, M. Komiya, Y. Hashimoto and H. OhashiDepartment of Quantum Engineering and Systems ScienceGraduate School of Engineering, The University of TokyoGood afternoon everybody, My name is Yu Chen. I am from University of Tokyo. The title of my talk is …
2 Contents of the Presentation Concerning the Price Fluctuation of Financial AssetsWhat are “stylized facts” ?Why do “stylized facts” occur ?How to utilize “stylized facts” ?My talk concersn the price fluctuation of financial assets, in particular those so-called stylized facts. Since most of you in this symposium are familiar with these issues. I will be as brief as possible.
3 What to Observe in the Market? The Asset PriceThe Price-ChangesReturnLog ReturnHere is the defition of the log-return.Nikkei 225 index from 1970 to Nikkei 225 consists of the 225 top-rated, blue-chip Japanese companies listed in the First Section of the Tokyo Stock Exchange.What Are Stylized Facts?
4 Stylized Facts Observed The Fat-Tailed Price DistributionThe Volatility ClusteringHere are two stylized facts, the fat-tailed distribution and the volatility clustering, observed in the foreign exchange market.Calculated from the minute data of Yen-Dollar rate,What Are Stylized Facts?
5 The Classic Theory for Financial Markets The Efficient Market Hypothesis (EMH) All information concerning a financial asset is already incorporated into the current price.The ImplicationsNo way to make risk-free profitCompletely rational tradersRandom-walk like price-changesIndependent Price-ChangesIdentical PDFsGaussian PDF for Price-ChangesThese stylized facts are at odds with the classical theory of financial markets. Typically, the efficient market hypothesis says that the distribution should Gaussian and there should be no correlation in price returns, no matter linear or nonlinear.What Are Stylized Facts?
6 The Fat-Tailed Distribution The Extraordinarily High RiskThe Universal ExistenceThe Power-Law DistributionLevyDistributionThe Six Sigma ProbabilityHowever the stylized facts are universal. These are the well-known results in econophysics.From Gopikrishna et al.CWhat Are Stylized Facts?
7 The Volatility Clustering Exponential Decay of the AutocorrelationThe Problem of EMHA Universal ExistenceJust another well-known results regarding the volatility clustering of S&P 500.What Are Stylized Facts?From Gopikrishna et al.C
8 Available Approaches to Analyze the Market Standard Finance TheoryThe Stochastic Differential EquationLimitationsBased on wrong assumptionsAwkward to describe traders’ behaviorsEconophysicsConcepts and TheoriesPhase transitionChaos, fractalSelf-organizationApproachesReplica methodNormalization group methodAgent-based simulationsEvolutionary computationsIf we review the recent work in econophysics, we find concepts and theories of statiscal mechanics and complex systems are being applied in the analysis of market. And the available approches are the following. We take the simulation approach.Why Do Stylized Facts Occur?
9 Simple Agent Model for Complex Price Dynamics Simplified Description of Traders’ ActivitiesNo way to model even one trader perfectlyEasier to analyze the market mechanismCollective Fluctuation Recovered to that of Price-ChangesThe large scale collective dynamics is often insensitive to small scale behaviorsSucceeded Examples in PhysicsSpin model for phase transitionPercolation model for critical phenomenaLattice gas model for fluid flowIn the simulation of market, we like to use those toy models, since we have some experience in simulation of fluid flow using the so-called lattice gas method. The method is very similar to the toy models of markets. Very simple in micro-dynamics neverthelsss can recover to certain extent the coarse-grained dynamics.Why Do Stylized Facts Occur
10 The Minority Game (MG) Parameters to Specify a Minority Game WIN A Multi-Agent, Multi-Strategy, Repeated GameThose Belonging to the Minority Win the GameParameters to Specify a Minority GamePlayer numberNumber of strategies for each playerMemory of the player+1WIN-1These are the basic minority games, I do not waste time here.00101-11011……Why Do Stylized Facts Occur?
11 Adaptive Learning in MG Some DefinitionsThe th agent’s bidThe total bid (excess demand)Score all the strategiesThe Adaptive Learning of AgentsAlso skip.Only those being minority get positive pay-offsWhat Do Stylized Facts Occur?
12 Characteristics of MG Basic Properties Volatility Predictability Congestion in strategy spaceEmergence of CooperationSymmetric to Asymmetric Phase TransitionThe macroscopic quantities to observe are these two, volatility and predictability. The control parameter ¥alpha is not so clearly defined. Since P can be a measure of the size of strategy pool, I put it as the congestion in strategy space.Why Do Stylized Facts Occur?
13 Relation between MG and Market Model 1 Time Evolution of an Idealized Market ModelTraders’ actions: strategic investment; position clearing; evaluation of strategiesAsset price / Traders’ capitalScores of investment strategiesAccording Marsili’s paper, the relationship between the original MG and a simple market model was clarified. In the market model, traders have three kinds of actions: strategic investment; position-clearing and strategy evaluation. The asset price and traders’ capital are updated every time, but scores of the investment strategies are updated every two time steps.
14 Relation between MG and Market Model 2 Details of the ModelTraders’ orderClear positionsPrice formationDemand and supplyBalance (D = S*p)Score the strategiesCapital updatesScore updatesDetails of these formulae are given in Marsili’s paper. So I shall not explain here, simply pointing out that a part of traders’ capital change is used in the update of strategies.
15 Relation between MG and Market Model 3 Simplification of the ModelSynchronization of tradersNeglect position-clearing and capital updatesUnderstanding the MG Market ModelPredict the future excess demandFundamentalists’ viewpointChartists’ viewpointStart from this simple model, if we further assume the synchronization of traders and neglect the position-clearing, the model can be reduced to the MG. There is also another way to reduce the model to MG without these assumptions. If we neglect the position-clearing and force the traders to evaluate their strategy right after the strategic investment, then traders have to predict the future excess demand. There are two ways to do this, according to Marsili’s paper, one is fundamentalists’ viewpoint and the other is the chartists’ viewpoint. From this, we know that the original MG market consists of pure fundamentalists.
16 Extension of the MG Market Model Two Kinds of Traders: Producers and SpeculatorsSpeculators have the right not to trade: GCMGDefinitionsProducerSpeculatorThe 0-StrategyPublic InformationThreshold for TradeLog-ReturnTrade VolumeScoring of the Strategies+1-1Ofcourse, in the real market, neither traders behave synchronously, nor would all of them be fundamentalists. We adopt a grand canonical MG market model suggested by Challet and Marsili. Characteristics of this model are the inclusion of two kinds of traders and the threshold for trades. Producers have only one strategy and do not have the ability to do adaptive learning. Speculators are like the agents in the original MG. Scores of speculators’ strategies are compared with a constant income represented by ¥epsilon. Only if scores became higher than this, speculators would join the market.Why Do Stylized Facts Occur?
17 Recovery of Stylized Facts Fat Tailed DistributionVolatility ClusteringWith certain set of parameters, the stylized facts can be recovered.Why Do Stylized Facts Occur?
18 Threshold’s Effect on Fat-Tailed Distribution Without the 0-StrategyWith the 0-StrategyThe mechanism behind the fat-tailed distribution was already explained by Challet and Marsili. There are two factors which influence the distribution form. First is the 0-strategy or the threshold, second is the congestion in strategy space. From the left figure, we see if the 0-strategy is switched off, no matter how we change the number of speculators it sticks to be an exponential distribution. However, in the right figure, if the 0-strateg is on, when there are enough number of speculators the fat-tailed distribution could emerge.Why Do Stylized Facts Occur?
19 The Effect of Speculation on Fat-Tailed Distribution Speculation causes larger fluctuationsA phase transition with the increase of speculatorsEffects of speculators are clearer in these figures. On the left, the fluctuation of price return (in red) is compared with the active number of speculators (in green). On the right, we can clearly see a phase change in the magnitude of price fluctuations when the number of speculators exceeds a critical value. At the critical vale, the -3 power law emerges.Where the -3 powerlaw emergesWhy Do Stylized Facts Occur?
20 Market Mechanism for Fat-Tailed Distribution The Important Role of ThresholdIn Model: the right not to playIn Real World: the Watch-And-Wait behavior of traders for various reasonsOther examples: Sand-Pile in SOC, Latent Heat ….The Congestion in the Strategy SpaceIn Model: the self-incurred phase transition caused by the similarity of agents’ strategies and the optimization of the strategies through the adaptive learningIn Real World: Traders often have similar strategies or they learn the similar strategiesWe can also explain the correspondences between the model and the real market. I skip this.Why Do Stylized Facts Occur?
21 The Effect of Np/Ns on VC Autocorrelation of the VolatilityThe Correlation Time of VolatilityWe investigate the relation between numbers of traders and the correlation time of absolute returns. In the simulation, volatility clustering appears sometimes and disappear some times. As we increase the number of producer and fix the number of speculator, the correlation time in volatility increases. As we increase the number of speculator and fix the number of producer the correlation time decreases. How to explain this? We suggested the following scenarios.Why Do Stylized Facts Occur?
22 Three Scenarios in the Modeled Market ProductionThe ProfitableChancese2e5e3e4ConsumptionIn the market producers produce profitable chances or the predictability of price return, and speculators consume these chances to earn money whenever possible. Depending on the relative number of speculator and producer, there could be three states, namely the chance rich state, the chance depleted state and the chance critical state. Volatility clustering show itself at the chance critical state.S1: Chance RichVC DisappearedS2: Chance CriticalVC EmergedS3: Chance DepletedVC DisappearedWhy Do Stylized Facts Occur?
23 Evidence 1 and 2 The increase of producer increases the predictability The increase of speculator decreases the predictabilityThese are evidences for the production of predictability and consumption of it.e1e2Why Do Stylized Facts Occur?
24 Evidence 3 and 4 e3 e4 When the number of speculator is Looking at the change of predictability of price return and the correlation of volatility simultaneously, we can find the following… (in captions of figures)When the number of speculator is(relatively) too small, the predictabilitybecomes high while the correlation lowWhen the number of speculator is(relatively) too large, the predictabilityis zero while the correlation decreases.Why Do Stylized Facts Occur?
25 Evidence 5When the predictability is just depleted , the maximum of correlation time of the absolute returns appears.e5Correlation time reaches its maximum right after the predictability is depletedWhy Do Stylized Facts Occur?
26 Market Mechanism for Volatility Clustering The Interaction between Different Types of AgentsIn Model: Producers generates the predictability (profitable chance); Speculators competitively consume itIn Real WorldProducers: Irrational Traders; Speculators: Rational TradersThe intelligent takes advantage of the others in financial marketThe Criticality of Phase Transition in Information SpaceIn Model: The maximum of time correlation emerges when the predictability is just depletedIn Real World: The market always seems like efficientAlso, we can relate things in the model to the real market. If this analysis is right, it means that the volatility clustering becomes one of the evidences for the criticality of financial market.Why Do Stylized Facts Occur?
27 Application of the Minority Game to Predicting Price The Goal: To predict price-changes in financial marketsIs It Predictable?Volatility clusteringThe predictabilityWhy Use Minority GameThe simple, built-in adaptive learningGA-like algorithm easily applicableWe tried to apply the MG to predict the price change. First, to answer the question whether the price is predictable we compares (in the right figure) the predictability of three kinds of time series against the time horizons.The Predictability of Time Series:GCMG market model; FX Market (only sign); and a spin model on network for stock marketHow to Utilize Stylized Facts?
28 optimization of strategy distribution The Predicting MethodFinancial MarketThe Modified Adaptive LearningData GenerationAnother MG simulationA random walkA GCMG SimulationA Network Stock Market Model SimulationFX Data ( )Black Boxcomplex mechanismGenerateReal market or artificial market generate time series data as a black box. A part of these data are used to train the predictor minority game. And the trained minority game are used to predict the remained part of data. First four datasets are generated by artificial markets. They are another MG, random walk, GCMG and a network model. The last one is the data generated by real market.LearningPredictPredictor MGMinority Gameoptimization of strategy distributionHow to Utilize Stylized Facts?
29 A Simple Preliminary Test To Predict Another MGComparison with the Prediction of a Random WalkIt seems reasonable that MG’s prediction of MG gives a good result, particularly compared with the meaningless prediction of a random walk. Correlations between the predicted data and those being predicted are shown in the right figure.How to Utilize Stylized Facts?
30 Two Further Tests To predict the time series generated by a GCMG To predict the time series generated by a network stock market modelThe same comparisons are done for MG predictions of GCMG and network model for stock market.How to Utilize Stylized Facts?
31 The Reason for the failure The bad performance in predicting the network market model is due to its poorness in recovering the stylized facts. In particular the volatility clustering is almost indetectable.The Price-Change DistributionAutocorrelation of VolatilityHow to Utilize Stylized Facts?
32 Prediction of the FX Market Finally, compared with the prediction of a random walk the prediction of MG to FX data are somewhat meaningful.How to Utilize Stylized Facts?
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