arXiv:1801.08222v1 [q-fin.CP] 24 Jan 2018 nnilAMmdl,w a loicueodrbook order include also Among can are. we truly they models, that ABM a [13] financial systems from them complex considering markets the and emulate as [10–12], and approach called bottom-up probe models pure of to class Multi-Agent (MAS) third sometimes Systems or a (ABMs) to seen Models leads Agent-Based traditionally This wealth microstructure the markets. explain in not of will approx- diversity and rough 9], and on [8, based reality are of they imations that say in- can system years. we to approach ference, the top-down over a results consider we promising models if However of of variety classes a two en- shown These have true [5–7]. emulate conditions and vironment to rigidities shocks market ra- stochastic the by exogenous replace hypothesis versions) Keynesian expectations New tional the learn- (in agent imperfect and for ing, and accounting rationality structure, re- bounded model add heteorgeneity, basic to the strive to models [4]. alism DSGE fluctuations of aggregate developments and Modern dynamics sectoral the agent-based for explicit provide mod- as which known (DSGE) are els Equilibrium second General The Stochastic strong. parameters Dynamic too the log-return not of is or variability calibration the 2] of as re- [1, long interesting as volatility [3] bring general forecasting can to These are pertaining series history. encountered times sults fit most to past and calibrated important like are first which three The models distinguish statistical models. historically of Among can classes dynamics. we markets financial these model to proaches h edo nneadeooishsue aiu ap- various used has and finance of field The .etrfrCgiinadDcso aig R ihrSho fEco of School Higher NRU Making, Decision and Cognition for 5.Center ahn erig epsuaeta uhAM ol ffrawh a offer would ABMs such that kno quanti postulate biases rational We implement behavioral autonomously learning. time machine and res same cognitive computational the at Syste specific a and Multi-Agent of with or lines endowed (ABM) main be Models the Agent-Based an via here neuroscience, behavior computational outline of We data form big the others. in and tre power study these of computational fields of increasing psychol base to artificial of of due the progress shift learning At the steady and neuropsychology, realism. the socia of of advances the th breakthroughs: range of of scientific new part weights major whole a the a by shifted ACE have critics given trends received recent also Yet time has ACE empiricism. met same successful of the the field to at the proximity its While for (ACE). researchers science Economics Computational based nttt o ol cnm n nentoa eain,Russian Relations, International and Economy World for Institute h itr frsac nfiac n cnmc a enwide been has economics and finance in research of history The .ntttdEued aCgiin S eerhUiest,75005, University, Research PSL Cognition, la de d’Etude 4.Institut .CF ainlRsac nvriyHge colo cnmc a Economics of School Higher University Research National 2.ICEF, tdsCgiie,EoeNraeSprer S nvriy ai F Paris University, PSL Superieure Normale Ecole Cognitives, Etudes .Lsag() .Blai() .BugosGrne34,B Gu B. 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Lussange(1), J. .GopfrNua hoy N NEMU6,Dpreetdes Departement U960, INSERM LNC Theory, Neural for Group 1. rgtftr o nnilaetbsdmodels agent-based financial for future bright A .ntttJa-io,EoeNraeSpeiue ai,FR Sup´erieure, Paris, Normale Ecole Jean-Nicod, 3.Institut Dtd aur 6 2018) 26, January (Dated: , etvl en h rc ftemre o uhsecurities such step for time market the the col- at of then price which the prices define transaction lectively at them matching and hsi iceetm loih aigi h trading the in [16]). taking books algorithm at order discrete-time bids auction a double an is a via a This as together as (such trading agents book those as order investors see modeled market are may ABM, traders financial some or a though In even approach. midway 15] [14, models prahsaewrh forattention. our Such of worthy agents. between are al- interactions approaches felt complex and more we assumption for crisis, optimization lows mod- the the Agent-based of with face [...] dispenses eling the tools. in In conventional help. further: by limited abandoned go of would models available I the fact, found I ” Trichet crisis, Jean-Claude 2010: the in [34]. instance play for to declared ABM for role stronger impact the [33]. of analysis structure ABMs in cross-market role the [32]. important of banks an central play of also to role can general tool quantitative the and policies, a regulatory easing, as market In taxes, impact popular trading the specifically, of [23–27]. became — [28–31] theory also game study ABM bi- especially years, way evolutionary and recent by 22], [20], emerged [21, models have ology learning models these psychological economics, of In 19]. vni Bsaeotndsge ihmn param- many with designed often are ABMs if Even rmargltr on fve,ti mle general a implies this view, of point regulatory a From [17– disciplines scientific many in used been have ABM oso hsc n hmsr o example, for chemistry and of hods nelgneadmr pcfial machine specifically more and intelligence g oad adsinedet the to due science hard a towards ogy t ua-optritrcin among interaction, human-computer d s eea ruet n potentially and arguments general ese hs w aeas on common found also have two These . n ffr fseicscrte rmalagents, all from securities specific of offers and aiefiaca taeisudtdby updated strategies financial tative nt h edo neuroeconomics, of field the to wn MS,weeec gn would agent each where (MAS), m ac td fcletv economic collective of study earch cec omnt o t akof lack its for community science l yipce ytefil fAgent- of field the by impacted ly l e ag frealism. of range new ole d r on w present-day two found are nds en oua mn natural among popular being t 1. + cdm fSciences of Academy ois ocwRussia Moscow nomics, dPrimakov nd ai,France Paris, tkin(1,5) rance saplc-ae during policy-maker a As ” eters and hence subject to the delicate issue of overfit- stylized facts. ting, one of their biggest advantages is that they require The importance of the universality of stylized facts to fewer assumptions (e.g normal of returns, really gauge financial markets comes from the fact that no-arbitrage) than top-down models [35]. Added to this, the price evolutions of different markets may have very ABM display the famous emergence proper different exogenous or endogenous causes. As a conse- to bottom-up approaches [36] and can hence show com- quence they highlight general underlying financial mech- pletely new regimes of transitions, akin to phase transi- anisms that are market-independent, and which can in tions in [37]. However, being models, turn be exploited for ABM architecture design. From ABMs are of course imperfect and need a thorough and a scientific point of view, stylized facts are hence ex- lengthy cross-market validation [38]. Yet at the same tremely interesting and their faithful emulation has been time, one should keep in mind that such a general and an active topic of research in the past fifteen years or cautious validation of ABMs shall be in fact applicable so [73, 74]. Their definite characteristics has varied ever and necessary to any other model as well [39]. so slightly over the years and across literature, but the From now on we consider the application of ABMs most widespread and unanimously accepted stylized facts to financial markets. We shall note that among finan- can in fact be grouped in three broad, mutually overlap- cial ABMs some exclusively pertain to high-frequency ping categories: trading [40, 41], while other take both high- and low- Non-gaussian returns: the returns distribution is non- frequency into account [42–44]. Another popular topic gaussian and hence asset prices should not be modeled of literature in financial ABMs is the emulation of the as brownian random walks [75, 76], despite what is taught widespread Minority Game [45, 46], which formally is in most text books, and applied in sell-side finance. In not a financial market problem, but a general game the- particular the real distributions of returns are dissim- ory problem which can be related to the financial issues ilar to normal distributions in that they are: (i) hav- of pricing and forecasting. ing fatter tails and hence more extreme events, with the In order to generate a dynamic trading activity in fi- tails of the cumulative distribution being well approx- nancial ABMs, a basic economic assumption is that the imated [75, 77] by a power law of exponent belonging agents disagree on the present security price or at to the interval [2, 4] (albeit this is still the subject of a different frequencies (which possibility is sometimes ex- discussion [78, 79] famously started by Mandelbrot [80] plicitly denied in economics literature [47]), and are hence and his Levy stable model for financial returns), (ii) neg- willing to long or short a same security at different prices. atively skewed and asymmetric in many observed mar- In other words, there must be some sort of price disagree- kets [81] with more large negative returns than large posi- ment happening and an original pricing mechanism at tive returns, (iii) platykurtic and as a consequence having the discretion of each individual agent. In the literature, less mean-centered events [82], (iv) with multifractal k- this mechanism of pricing in financial ABMs has in gen- moments so that their exponent is not linear with k, as eral been designed according to two basic mechanisms seen in [83–86]. of trading: in some models at least a part of the agents trade in a random way as ‘noise traders’ [40, 41, 48–52], Clustered volatilities: market volatility tends to aggre- and in other models agents use realistic trading strate- gate or form clusters [2]. Therefore compared to av- gies known to real financial markets, depending on the erage, the to have a large volatility in the variability and stochasticity of the market [53–56]. near-future is greater if it was large also in the near- past [73, 87, 88]. Regardless of whether the next return is positive or negative, one can thus say that large (resp. small) return jumps are likely followed by the same [80], I. ACCURACY and thus display some sort of long memory behavior [89]. Because volatilities and trading volumes are often corre- Over the years, economic research (and especially lated, we also observe a related volume clustering. econophysics research) has gradually discovered a certain Decaying auto-correlations: the auto-correlation function number of non-trivial statistical features of or stylized of the returns of financial time series are basically zero facts about financial times series. These stylized facts for any of the auto-correlation lag, except for very are based on variations in prices that have universal sta- short lags (e.g. half-hour lags for intraday data) because tistical properties in common from market to market, of a mean-reverting microstructure mechanism for which over different types of instruments, and time periods. there is a negative auto-correlation [81, 89]. This is some- Among these, those pertaining to returns distribution times feeding the general argument of the well-known Ef- or volatility clustering for example were gradually dis- ficient Market Hypothesis [90, 91] that markets have no covered during the nineties: Kim-Markowitz [57], Levy- memory and hence that one cannot predict future prices Levy-Solomon [58–64], Cont-Bouchaud [65], Solomon- based on past prices or information [87, 88]. According Weisbuch [66], Lux-Marchesi [53, 67], Donangelo- to this view, there is hence no opportunity for arbitrage Sneppen [68–71], Solomon-Levy-Huang [72]. It was also within a financial market [77]. It has been observed how- not before this time that ABM started to emulate these ever that certain non-linear functions of returns such as squared returns or absolute returns display certain steady III. TRENDS auto-correlations over longer lags [89]. As previously said, emergence and recent progress of Since then, ABMs of financial markets have steadily two separate fields of research will likely have a ma- increased in realism and can generate progressively more jor upcoming impact on economic and financial ABMs. robust scaling experiments. We can specifically highlight The first one is the recent developments in cognitive the potential of these simulations to forecast real financial neuroscience and neuroeconomics [104–108], which has time series via reverse-engineering. A promising recent revolutionized with its ever lower perspective for such use of ABMs has been highlighted in cost experimental methods of functional magnetic reso- the field of by [92–94]: the agent-based model nance imaging (fMRI), electro-encephalography (EEG), parameters are constrained to be calibrated and fit real fi- or magneto-encephalography (MEG) applied to deci- nancial time series and then allowed to evolve over a given sion [109, 110] and game theories [111]. The second time period as a basic forecast measure on the original one concerns the recent progress of machine learning time series used for calibration. With this, one could thus which has been possible in the last few years by the say that ABMs are now reaching Friedman’s [95] method- improved computer power, and especially GPU comput- ological requirement that a theory must be ”judged by its ing [112], as well as the availability of big data to train predictive power for the class of phenomena which it is supervised algorithms and reach in some tasks superhu- intended to explain.” man performance [113–116]. Among the multiple ma- chine learning approaches and algorithms, we can high- light in particular the recent progress of reinforcement learning [117–119], artificial neural networks [120–122], Monte Carlo tree search [115], and multi-agent learn- ing [114, 123, 124]. Furthermore, these have been com- II. CALIBRATION bined to work together in new types of unsupervised al- gorithms that have given impressive results [125, 126], raising concern about the scale of general societal impact Just as any other model, the parameters of the ABM of artificial intelligence [127]. must be calibrated to real financial data in order to per- To the ABM field, this implies that the realism of form realistic emulation. This part of calibration is to- the economic agents can be greatly increased via these gether with architecture design the most technical and two recent technological developments: the agents can crucial aspect of the ABM [96]. Yet at the same time be endowed with numerous cognitive and behavioral bi- in the literature most calibration techniques are done by ases emulating those of human investors for instance, but hand, so that the stylized facts are re-enacted in a satis- also their trading strategies can be more faithful to real- factory way. Therefore so far the ABM calibration step ity in the sense that they can be dynamic and versatile is often performed in way that is sub-optimal [48, 97, 98]. depending on the general stochasticity or variability of On the other hand, an efficient methodology for cal- the market, thanks to the fact that via machine learning ibration would need two important steps. First a fully they will learn to trade and invest. At a time where the automated meta-algorithm in charge of the calibration economy and financial markets are progressively more should be incorporated, so that massive amount of fi- and more automated, this impact of machine learning nancial data could be treated and the aforementioned on ABM should thus be explored. One should keep in scope of validity of ABM studied via cross-market vali- mind that the central challenge (and in fact hypothe- dations [48, 99]. This is important as the robustness of ses) of ABM are the realism of the agents, but also the a calibration always relies on many runs of ABM sim- realism of the economic transactions and interactions be- ulations [100]. Second, this calibration meta-algorithm tween the agents. should be working through the issues of overfitting and underfitting, which may constitute a severe challenge due to the ever-changing stochastic nature of financial mar- IV. APPLICATION kets.

Part of this calibration problem is to thoroughly and Besides studying the agents’ collective trading interac- cautiously define the parameter space. This step is par- tions with one another, an ABM stock market simula- ticularly sensitive, since it can lead to potentially prob- tion could be used to probe the following specific fields lematic simplifications. For instance, what should be the of study: size of the time step of the simulation? ABM with a daily Market macrostructure: one could study how human cog- time tick will of course produce time series that are much nitive and behavioral biases change agents’ behaviour at coarser than those coming from real financial data, which a level of market macrostructure. The two main topics include all sorts of intraday events [101–103]. of market macrostructure that would be of are naturally all those pertaining to systemic [128, 129] (bubble and crash formation, problem of illiquidity), and Credit risk: one could study the effect of market evolu- also those related to herding-type phenomena [130] (in- tionary dynamics when the agents are allowed to learn formation cascades, rational imitation, reflexivity). A and improve their trading strategy and cognitive biases key aspect of this work would be also to carefully cali- via machine learning. In other words, it would be inter- brate and compare the stylized facts to real financial data esting to see the agents population survival rates [139– (we need to see standardized effects such as volatility 141] (cf. credit risk), and overall price formation with re- clustering, leptokurtic log-returns, fat tails, long mem- spect to the arbitrage-free condition of markets when we ory in absolute returns). Indeed some of these macro- increase the variability of the intelligence in the trading effects have been shown to arise from other agent-based agents [142]. Indeed, recent studies [133, 143, 144] sug- market simulators [11, 131], however it is not yet fully un- gest that arbitrage opportunities in markets arise mainly derstood how these are impacted by the agents learning from the collective number of non-optimal trading deci- process nor their cognitive and behavioral biases such as sions that shift the prices of assets from their fundamen- , greed, cooperativity, intertemporality, and tal values via the law of . Another the like. topic would be to compare such agent survivability with Price formation: one could study how these biases Zipf’s law [141]. change the arbitrage possibilities in the market via their blatant violation of the axioms of the Efficient Market V. CONCLUSION Hypothesis [132]. Indeed agent-based market simulators so far have often relied on the use of the aforementioned We have thus highlighted new possible exciting per- ’noise traders’ in order to generate the necessary con- spectives for financial ABM, where the agents would be ditions for basic business activity [12, 33, 133]. The designed with neuroeconomic biases and having trading novel aspect here would be to go one step further and or investment strategies updated by machine learning. replace this notion of purely random trading by imple- One should recall that the main argument against ABM, menting specific neuroeconomic biases common to real and indeed their main challenge, has always been about human behaviors. Another problem of past research in the realism of the agents, albeit one should also consider agent-based stock market simulators is that these have the realism of the economic transactions. We thus argue often relied on agents getting their information for price that these recent trends should set a totally new level of forecasting from a board of technical indicators common realism for financial ABM to all agents [134]. In contrast, we should develop agent In particular, whereas early financial ABM generations models that allow each agent to be autonomous and use increased their realism of emulation of real stock markets and ameliorate its own forecasting tools. This is a crucial by re-enacting stylized facts gradually during the late aspect in view of the well-known fact that information is nineties, and whereas the issue of calibration is still un- at the heart of price formation [135]. We hypothesize dergoing the process of automation so that ABM may be that such agent learning dynamics is fundamental in ef- validated on large scales of data, we expect these trends fects based on market reflexivity and impact on price to bring in several revolutionary breakthroughs, and the formation, and hints to the role played by fundamental emergence and recognition of ABM as the relevant tools pricing versus technical pricing of assets. Of major inter- that they are in finance and economics. est is the issue of global market liquidity provision and Aknowldgement: This work was supported by the its relation to the law of supply and demand and bid-ask RFFI grant nr.16-51-150007 and CNRS PRC nr.151199. spread formation [136–138].

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