Article

# Does the Market Maker Stabilize the Market?

Authors:
• Shanghai Univeristy of Finance and Economics
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## Abstract

The market maker plays an important role in price formation, but his/her behavior and stabilizing impact on the market are relatively unclear, in particular in speculative markets. This paper develops a financial market model that examines the impact on market stability of the market maker, who acts as both a liquidity provider and an active investor in a market consisting of two types of boundedly rational speculative investors—the fundamentalists and trend followers. We show that the market maker does not necessarily stabilize the market when he/she actively manages the inventory to maximize profits, and that rather the market maker’s impact depends on the behavior of the speculators. Numerical simulations show that the model is able to generate outcomes for asset returns and market inventories that are consistent with empirical findings.

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... Second, the market clearing mechanism used in this paper is via a market maker who provides liquidity to the market. It is well known that (see, for example, Bradfield, 1979) the market maker acts not only as a liquidity provider but also as an active investor by managing the market maker inventory in order to maximize the profit (see, for example, Zhu, Chiarella, He and Wang, 2009). To incorporate the market maker inventory into the present framework and to examine the market impact of the time delay are of interest. ...
... It should be stressed that the double edged role on the stability of time delay is not new in applied mathematical literature, in particular in mathematical biology literature, see for exampleMacDonald (1978) andBeretta, Bischi and Solimano (1988).2 In a recent paper byZhu, Chiarella, He and Wang (2009), the roles of the market maker as both liquidity provider and investor are examined and it is found that, in some market conditions, the market maker has an incentive to destabilize the market. ...
... When the supply is positive but constant, the fundamental price needs to be adjusted to have the same price dynamics, see for example,Zhu, Chiarella, He and Wang (2009). ...
Article
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Within a continuous-time framework, this paper proposes a stochastic heterogeneous agent model (HAM) of financial markets with time delays to unify various moving average rules used indiscrete-time HAMs. The time delay represents a memory length of a moving average rule indiscrete-time HAMs.Intuitive conditions for the stability of the fundamental price of the deterministic model in terms of agents' behavior parameters and memory length are obtained. It is found that an increase in memory length not only can destabilize the market price, resulting in oscillatory market price characterized by a Hopf bifurcation, but also can stabilize another wise unstable market price, leading to stability switching as the memory length increases. Numerical simulations show that the stochastic model is able to characterize long deviations of the market price from its fundamental price and excess volatility and generate most of the stylized factso bserved in financial markets.
... To the best of our knowledge, Westerhoff [27] has been the first to analyse how inventory management of foreign exchange dealers may affect exchange-rate dynamics. Later on, Zhu et al. [31] developed a model consisting of a market with two different groups of agents (fundamentalists and chartists) plus a market maker acting both as a dealer and an active investor, showing that 'the market maker does not necessarily stabilize the market when actively manages his/her inventory to maximize the profit' ( [31] p. 3165). Modeling market makers may make the dynamics much easier because a parameter, the market maker reaction coefficient, is added. ...
... To the best of our knowledge, Westerhoff [27] has been the first to analyse how inventory management of foreign exchange dealers may affect exchange-rate dynamics. Later on, Zhu et al. [31] developed a model consisting of a market with two different groups of agents (fundamentalists and chartists) plus a market maker acting both as a dealer and an active investor, showing that 'the market maker does not necessarily stabilize the market when actively manages his/her inventory to maximize the profit' ( [31] p. 3165). Modeling market makers may make the dynamics much easier because a parameter, the market maker reaction coefficient, is added. ...
... The main goal of the paper is the analysis of the role of the inventories within a framework characterized by just two groups of fundamentalists, evaluating, at the same time, the role of a market maker when acts as both dealer and liquidity provider. Therefore, we add the market maker inventory to the framework of Naimzada and Ricchiuti [23] and, unlike Zhu et al. [31], we analyze the double role of the market maker. In this way, we can study the interaction between heterogeneous fundamentalists and the market maker with these two functions. ...
Article
In this paper we develop an heterogenous agents model of asset price and inventory with a market maker who considers the excess demand of two groups of agents that employ the same trading rule (i.e. fundamentalists) with different beliefs on the fundamental value. The dynamics of our model is driven by a bi-dimensional discrete non-linear map. We show that the market maker has a destabilizing role when she actively manages the inventory. Moreover, inventory share and the distance between agents' beliefs strongly influence the results: market instability and periodic, or even, chaotic price fluctuations can be generated. Finally, we show through simulations that endogenous fluctuations of the fractions of agents may trigger to instability for a larger set of the parameters.
... Equivalent results are obtained by Carraro and Ricchiuti (2015) and Zhu et al. (2009), who consider market makers that take speculative positions by adjusting their inventories toward a given exogenous target. These models don't derive the pricing rule from an optimizing behavior of the market maker, instead they rely on ad hoc pricing mechanisms. ...
... My model confirms the main result of Hommes et al. (2005) while, on the other hand, it shows that the market maker has conflicting effects on the stability of the market. From this perspective, my results converge with those of Zhu et al. (2009) andCarraro andRicchiuti (2015), who also underline that the market maker destabilizes the market when she manages aggressively her inventory. On the other hand, these works provide analytical results which are restricted to the case of fixed proportions of speculators, while my results are derived using the heuristic switching mechanism of BH98 which allows these proportions to evolve endogenously. ...
Article
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I introduce an optimizing monopolistic market maker in an otherwise standard setting à la Brock and Hommes (J Econ Dyn Control 22(8–9):1235–1274, 1998) (BH98). The market maker sets the price of a zero-yielding asset taking advantage of her knowledge of speculators’ demand, manages her inventory of the asset and eventually earns profits from trading. The resulting dynamic behavior is qualitatively identical to the one described in BH98, showing that the results of the latter are independent from the institutional framework of the market. At the same time, I show that the market maker has conflicting effects. She acts as a stabilizer when she allows for market imbalances, while she acts as a destabilizer when she manages aggressively her inventories and when she trades, especially if she acts as fundamentalist or if she is a strong extrapolator. Indeed the more stable institutional framework is one in which the market makers are inventory neutral and doesn’t trade but, even in this case, the typical complex behavior of BH98 occurs.
... whereĪ is the autonomous component of investments, γ > 0 relates to the accelerator component, a 1 and a 2 are positive parameters that determine the investment function variation range and ϕ ≤ 0. It is worth noting that a functional form as the one proposed here for the investments function is in line with the classic macroeconomic literature of the 1930s-1950s (see, e.g., [1], [3], [28]). Moreover, the motivation for considering a sigmoid function to model a component of the investments comes from the Hicks' idea of embodying a floor and a ceiling in the evolution of investments, in order to take into account the impossibility of an indefinite growth and disinvestment due to resource and physical constraints (see [5,13,29] and [30]). Finally, expression (4) also states that investments negatively depend on the interest rate, being ϕ ≤ 0. In fact, the interest rate reflects the cost of borrowing in order to finance investment projects and, other things being equal, as the interest rates rise, financing new investment projects becomes more expensive. ...
... Combining (28) and (31) we obtain condition (12a), while (29) and (32) together provides (12b). ...
Article
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In this paper we consider a nonlinear model for the real economy described by a multiplier–accelerator setup. The model comprises the government sector, which influences the output dynamics by means of the fiscal policy, and the money market, where the money supply depends upon the fluctuations in the economic activity. Through rigorous analytical tools combined with numerical simulations, we investigate the stability conditions of the unique steady state and the emergence of different kinds of endogenous dynamics, which are the results of the action of the fiscal and the monetary policy through their reactivity degrees. Such policies, if properly tuned, can lead the economy toward the desired full employment target but, on the other hand, can also generate endogenous fluctuations in the pace of the economic activity, associated with the occurrence of closed invariant curves and multistability phenomena.
... To convince readers the relevance of our model in …tting the …nancial markets, we calibrate our two-market model to match the stylized facts of …nancial markets following the practice of the extant literature, e.g. Westerho¤ and Dieci (2006), Zhu et al. (2009), Schmitt and Westerho¤ (2017a), Schmitt and Westerho¤ (2017b, just to cite a few. According to Cont (2001), Lux and Ausloos (2002) and Westerho¤ and Dieci (2006), real-world speculative markets have following characteristics: (1) volatility cluster phenomena in which high-volatility events tend to cluster in time; ...
... Autocorrelation of return is insigni…cant across lags generally while autocorrelation of absolute returns is signi…cant (Fig. 9). These stylized facts calibrations are similar to Zhu et al. (2009). In addition, at 95% con…dence interval, there is signi…cant cross-correlation at di¤erent lags. ...
Article
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Inspired by the empirical findings, we include international traders to capture linkage between markets and propose a two-market heterogeneous agents model to simulate financial crisis with contagion effect. This paper manages to calibrate sudden crash behavior of US and UK stock markets during “Black Monday” of 1987 besides smooth crisis and disturbing crisis categorized in literature. It is implied that financial crisis and its contagion could be endogenous, which supports a scenario of over-valuation causing a financial crisis. In addition, the model shows that financial system could be fragile in which small shock(s) hitting individual market's fundamental could cause financial crisis spreading to the other market. This also supports a scenario of external shock triggering a financial crisis. Lastly, to demonstrate the relevance of our model to financial markets, we manage to match typical stylized facts, especially cross-correlation which is exclusive to a multiple-market case.
... The volatility of the news arrival process is quantified by σ(r f ), which is the standard deviation of the fundamental log-return, whereas the volatility of the market can be measured a posteriori as the standard deviation of logreturn, σ(r). The order of magnitude of the volatility of log-return may be quite different from that of the input noise representing news arrivals reflected in the fundamental value, expressed by the inequality σ(r) > σ(r f ) [69,70,71,56,72]. [56] states that it is difficult to justify the volatility in asset log-return by variations in fundamental economic variables. Hence, the volatility of the arrival of new information on the market cannot explain returns volatility. ...
Preprint
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This paper proposes a methodology to empirically validate an agent-based model (ABM) that generates artificial financial time series data comparable with real-world financial data. The approach is based on comparing the results of the ABM against the stylised facts -- the statistical properties of the empirical time-series of financial data. The stylised facts appear to be universal and are observed across different markets, financial instruments and time periods, hence they can serve to validate models of financial markets. If a given model does not consistently replicate these stylised facts, then we can reject it as being empirically inadequate. We discuss each stylised fact, the empirical evidence for it, and introduce appropriate metrics for testing the presence of these in model generated data. Moreover we investigate the ability of our model to correctly reproduce these stylised facts. We validate our model against a comprehensive list of empirical phenomena that qualify as a stylised fact, of both low and high frequency financial data that can be addressed by means of a relatively simple ABM of financial markets. This procedure is able to show whether the model, as an abstraction of reality, has a meaningful empirical counterpart and the significance of this analysis for the purposes of ABM validation and their empirical reliability.
... Since in the present work we allow a 1 and a 2 to be possibly different, we can deal with more general settings in which the market maker can react in a different manner to a positive or to a negative excess demand. We recall that nonlinear adjustment mechanisms determining a bounded price variation and similar to the one on the right-hand side of (2.5) have been already considered in Chiarella et al. (2009), Naimzada andPireddu (2015b, c), Naimzada and Ricchiuti (2014), Tuinstra (2002) and Zhu et al. (2009). ...
Article
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We propose a financial market model with optimistic and pessimistic fundamentalists who, respectively, overestimate and underestimate the true fundamental value due to ambiguity in the stock market. We assume that agents form their beliefs about the fundamental value through an imitative process, considering the relative ability shown by optimists and pessimists in guessing the realized stock price. We also introduce an endogenous switching mechanism, allowing agents to switch to the other group of speculators if they performed better in terms of relative profits. Moreover, the stock price is determined by a nonlinear mechanism. We study, via analytical and numerical tools, the stability of the unique steady state, its bifurcations and the emergence of complex behaviors, with possible multistability phenomena. To quantify the global propensity to optimism/pessimism of the market, we introduce an index, depending on pessimists’ and optimists’ beliefs and shares, thanks to which we are able to show that the occurrence of the waves of optimism and pessimism are due to the joint effect of imitation and switching mechanism. Finally, we perform a statistical analysis of a stochastically perturbed version of the model, which high lights fat tails and excess volatility in the returns distributions, as well as bubbles and crashes for stock prices, in agreement with the empirical literature.
... The bifurcations occurring in a piecewise-smooth system may be quite di¤erent from those occurring in a smooth one. In fact, in the case of a piecewise-linear system (as in our model) the existing bifur- 2 Such a modelling device is also used in Zhu et al. (2009). cations are either border-collision 3 or contact bifurcations 4 , as the local bifurcations associated with the eigenvalues are always degenerate. ...
Article
We develop a financial market model with heterogeneous interacting agents: market makers adjust prices with respect to excess demand, chartists believe in the persistence of bull and bear markets and fundamentalists bet on mean reversion. Moreover, speculators trade asymmetrically in over- and undervalued markets and while some of them determine the size of their orders via linear trading rules others always trade the same amount of assets. The dynamics of our model is driven by a one-dimensional discontinuous map. Despite the simplicity of our model, analytical, graphical and numerical analysis reveals a surprisingly rich set of interesting dynamical behaviors.
... For both market members, autocorrelation of returns tend to be insignificant across lags except for the first few lags, while the ones of absolute returns are significant and decrease slowly with lags. These autocorrelation behaviors are similar to Zhu et al. (2009). Fig. 7 examines cross-correlation of return between the two market members. ...
Article
With the development of globalization and regional economic integration, regional markets linked with a common currency emerge, in which investors from domestic market are allowed to trade in foreign markets. Empirical studies have evidenced extensively the existence of co-movement of asset prices or cross-correlation in market returns among these markets, especially in global event. However, there is no theoretical model in literature that can provide economically plausible justifications for these stylized facts. This research intends to fill up such a gap with a simplest possible nonlinear dynamic model. Based on the classical market-maker framework of Day and Huang (1990), a two-market HAM model is developed, which does not only prove in theory the existence of price co-movement but also replicate in simulation this typical characteristic, along with other well known stylized facts characterizing individual financial market. Moreover, theoretical analysis suggests meaningful implications for market opening policy. In particular, in terms of financial stability, a relatively small market may not benefit from market linkage and market opening is essentially a double-edged sword.
... Much more could (and should) be done to model the behaviour and incentives of the market maker. Zhu et al. (2009) analyse a model that takes into account the inventory of the market maker. ...
Article
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This article surveys boundedly rational heterogeneous agent (BRHA) models of financial markets. We give particular emphasis to the role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, and calibration of this class of models. Due to agents' behavioural features and market noise, the BRHA class of models are both non-linear and stochastic. We show that BRHA models produce both a locally stable fundamental equilibrium corresponding to that of the standard paradigm, as well as instability with a consequent rich range of possible complex behaviours that are analysed by both simulation and deterministic bifurcation analysis. A calibrated model is able to reproduce quite well the stylised facts of financial markets. The BRHA framework seems able to better accommodate market features such as fat tails, volatility clustering, large excursions from the fundamental and bubbles than the standard financial market paradigm.
... To some extent differences in practice are a reflection of context and depend to a large extent upon the specific nature of the markets in question, customs and regulatory environment, prompting some to begin new work on the behavioural typologies of market makers and the corresponding character of the markets they make (e.g. Zhu, Chiarella, He, & Wang, 2009). As a result, the strength of the market makers' position and their stabilising influence may vary, giving rise to different market characteristics in each case. ...
Article
Planning has been widely vilified for the role it plays in disrupting the development process, hindering economic growth and creating the conditions for undersupply in housing markets, characterised by unaffordability. In this paper we hope to show that the analyses that support this view of planning are incomplete because of the theoretical limitations of the neoclassical tradition from which they emerge. By way of alternative we posit an account of planning that draws upon game theory and behavioural economics to explore those aspects of the activity that serve to animate the development process. This interpretation of planning as a " market maker " is explored through empirical case study research from three continental European contexts where planning is charged with playing an economically active role to control liquidity.
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... – Models taking account of M M inventory have been developed (eg. Chiarella et al. (2009)). ...
Article
This chapter surveys the boundedly rational heterogeneous agent (BRHA) models of financial markets, to the development of which the authors and several co-authors have contributed in various papers. We give particular emphasis to role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, portfolio implications, the impact of stochastic elements on the markets dynamics, and calibration of this class of models. Due to agents? behavioural features and market noise, the BRHA models are both nonlinear and stochastic. We show that the BRHA models produce both a locally stable fundamental equilibrium corresponding to that of standard paradigm, as well as instability with a consequent rich range of possible complex behaviours characterised both indirectly by simulation and directly by stochastic bifurcations. A calibrated model is able to reproduce quite well the stylized facts of financial markets. The BRHA framework is thus able to accommodate market features that seem not easily reconcilable for the standard financial market paradigm, such as fat tail, volatility clustering, large excursions from the fundamental and bubbles.
... Penelitian sebelumnya tentang market maker yang telah didokumentasikan secara luas. Misalnya, Zhu et al. (2009) melihat dua kategori investor yaitu investor spekulatif (yang sangat rasional dan fundamentalis) dan investor yang mengikuti tren, untuk melihat bagaimana pembuat pasar mempengaruhi stabilitas pasar. Temuan menunjukkan bahwa pembuat pasar memainkan peran penting dalam penciptaan harga, bahkan jika perilaku dan pengaruh mereka terhadap stabilitas pasar belum diketahui, terutama di pasar spekulatif yang mengandalkan perilaku spekulan. ...
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p> Abstract : Our research focuses on herding behavior and broker summary analysis in the Covid-19 time frame in Indonesia. Herding behavior in the retail exchange community or the general public is considered detrimental due to the irrationality of analysis and promoting euphoria which results in very large losses. Answering the research gap, we offer a broad exploration concept to avoid and create positive returns by utilizing the herding behavior of the retail market community. We tested using multiple methods to ensure the existence of herding behavior in a regression setting of two and took advantage of positive opportunistic returns for exchange play. The first method shows that the research sample detected herding behavior during March 11, 2020 – March 11, 202 and we ensure the resilience of existence through two models. The second method, to get a positive return, we offer bandarmology analysis adopted from Dow theory for trading in a market maker style. Analyzing the movement and following market makers, we can conclude that it creates positive returns and prevents the stock exchange community from the impact of sustainable auto rejects. This study has limitations, for future research we expect the use of empirical models that are simpler and more efficient in revealing herding behavior. Furthermore, for the exploratory method, further research can be carried out in disclosing bandarmology analysis based on stock categorization (blue chip, second liner, and third liner), time horizon of market makers, and detailed analysis of camouflage behavior of market makers using retail securities. Keywords : bandarmology ; brokers summary; herding behavior; market makers </p
... The price variation limiter mechanism can be modeled by a sigmoidal adjustment rule that determines a bounded price variation in every time period due to the presence of two asymptotes that limit the price changes. In the literature on behavioral financial markets, nonlinear price adjustment mechanisms have already been considered, among others, by Tuinstra (2002) and Zhu et al. (2009). ...
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Chapter
Mathematical models apply mathematical ways of thinking to simplify and abstract problems needing to be solved, and use mathematical symbols, formulas, diagrams to describe the essential characteristics and inherent rules of things. When people solve a specific problem, they do not rely on observations and experiments, but turn the problem into a mathematical topic and use mathematical analytic method to find the answer. For example, the variations of the electric current and voltage of a circuit system do not need to be actually measured, but are obtained by establishing a mathematical model of differential equation according to the laws of electromagnetics, and then substituting known data for the unknowns in the model for a solution.
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Heterogeneous beliefs have been widely regarded as the basic premise for construction of asset pricing models. By taking the market maker scenario as market clearing mechanism, a heterogeneous asset pricing (HAP) model with market maker is constructed and investigated in this paper. The bifurcation theory is applied to analyze the underling deterministic system and the wavelet analysis is used to study the stochastic model. The study shows that the asset price dynamics is highly associated with the behavior of the market maker, the level of activity of the fundamentalists and trend followers.
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In this paper, we propose a financial market model with heterogeneous speculators, i.e., optimistic and pessimistic fundamentalists that, respectively, overestimate and underestimate the true fundamental value due to ambiguity in the stock market, which prevents them from relying on the true fundamental value in their speculations. Indeed, we assume that agents use in its place fundamental values determined by an imitative process. Namely, in forming their beliefs, speculators consider the relative profits realized by optimists and pessimists and update their fundamental values proportionally to those relative profits. Moreover, differently from the majority of the literature on the topic, the stock price is determined by a nonlinear mechanism that prevents divergence issues. For our model, we study, via analytical and numerical tools, the stability of the unique steady state, its bifurcations, as well as the emergence of complex behaviors. We also investigate multistability phenomena, characterized by the presence of coexisting attractors.
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In this chapter, we provide a survey of research on scaling phenomena in financial data pursued by physicists and compare their methodology and results with the approach of economists dealing with the same topic. We also try to put this work into perspective by discussing in how far it is reconcilable with traditional models in finance (the efficient market hypothesis) or whether it leads to a new viewpoint on market interactions.
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Long-range dependence in volatility is one of the most prominent examples in financial market research involving universal power laws. Its characterization has recently spurred attempts to provide some explanations of the underlying mechanism. This paper contributes to this recent line of research by analyzing a simple market fraction asset pricing model with two types of traders – fundamentalists who trade on the price deviation from estimated fundamental value and trend followers whose conditional mean and variance of the trend are updated through a geometric learning process. Our analysis shows that agent heterogeneity, risk-adjusted trend chasing through the geometric learning process, and the interplay of noisy fundamental and demand processes and the underlying deterministic dynamics can be the source of power-law distributed fluctuations. In particular, the noisy demand plays an important role in the generation of insignificant autocorrelations (ACs) on returns, while the significant decaying AC patterns of the absolute returns and squared returns are more influenced by the noisy fundamental process. A statistical analysis based on Monte Carlo simulations is conducted to characterize the decay rate. Realistic estimates of the power-law decay indices and the (FI)GARCH parameters are presented.
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This paper is a contribution to the literature on the explanatory power and calibration of heterogeneous asset pricing models. We set out a new stochastic market-fraction asset pricing model of fundamentalists and trend followers under a market maker. Our model explains key features of financial market behaviour such as market dominance, convergence to the fundamental price and under- and over-reaction. We use the dynamics of the underlying deterministic system to characterize these features and statistical properties, including convergence of the limiting distribution and autocorrelation structure. We confirm these properties using Monte Carlo simulations.
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The authors are indebted to the anonymous referee for a very detailed and insightful report on an earlier version of this paper that has led to many improvements in the current version. Address correspondence to: Tony He, School of Finance and Economics, University of Technology, Sydney, P.O. Box 123 Broadway, NSW 2007, Australia; e-mail: tony.he1@uts.edu.au.This paper studies the dynamics of a simple discounted present-value asset-pricing model where agents have different risk attitudes and follow different expectation formation schemes for the price distribution. A market-maker scenario is used as the market-clearing mechanism, in contrast to the more usual Walrasian scenario. In particular, the paper concentrates on models of fundamentalists and trend followers who follow recursive geometric-decay (learning) processes (GDP) with both finite and infinite memory. The analysis depicts how the dynamics are affected by various key elements (or parameters) of the model, such as the adjustment speed of the market maker, the extrapolation rate of the trend followers, the decay rate of the GDP, the lag length used in the learning GDP, and external random factors.
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In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete time stationary model in terms of return and wealth proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents the stationary model can have multiple steady-states. The steady-state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to steady-state follows an optimal slection principle - the return and wealth proportions tend to the steady-state which has relatively higher return. More importantly, heterogeneity can generate instability which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from time to time. To model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous time finance, in that the asset price is fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed asets returns.
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Adaptively rational equilibrium is introduced, where agents adapt their beliefs by choosing from a finite set of predictor functions. Agents make a rational predictor choice, based upon a publically available performance measure such as realized past profits. This results in an adaptive belief system, where predictor choice is coupled to the market equilibrium dynamics. As a typical example, the cobweb model with rational versus naive expectations is analyzed. If the market is locally unstable and rational expectations are costly to obtain, a high intensity of choice for predictor selection leads to chaos and strange attractors.
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Financial markets (share markets, foreign exchange markets and others) are all characterized by a number of universal power laws. The most prominent example is the ubiquitous finding of a robust, approximately cubic power law characterizing the distribution of large returns. A similarly robust feature is long-range dependence in volatility (i.e., hyperbolic decline of its autocorrelation function). The recent literature adds temporal scaling of trading volume and multi-scaling of higher moments of returns. Increasing awareness of these properties has recently spurred attempts at theoretical explanations of the emergence of these key characteristics form the market process. In principle, different types of dynamic processes could be responsible for these power-laws. Examples to be found in the economics literature include multiplicative stochastic processes as well as dynamic processes with multiple equilibria. Though both types of dynamics are characterized by intermittent behavior which occasionally generates large bursts of activity, they can be based on fundamentally different perceptions of the trading process. The present paper reviews both the analytical background of the power laws emerging from the above data generating mechanisms as well as pertinent models proposed in the economics literature.
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Most exchanges in a decentralized economy are mediated by agents who make markets. This paper applies the elementary theory of such mechanisms to equity markets. Based on stylized institutional and behavioral facts and exploiting the methods of nonlinear dynamics, it explains salient properties of stock market dynamics.
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There has been renewed interest in power laws and various types of self-similarity in many financial time series. Most of these tests are visual in nature, and do not consider a wide range of possible candidate stochastic models capable of generating the observed results in small samples. This paper presents a relatively simple stochastic volatility model, which is able to produce visual power laws and long memory similar to those from actual return series using comparable sample sizes. These are small-sample features for the stochastic volatility model, since asymptotically it possesses none of these properties. The primary mechanism for this result is that volatility is assumed to have a driving process with a half life that is long relative to the tested aggregation ranges. It is argued that this might be a reasonable feature for financial, and other macroeconomic time series.
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This paper examines how inventory management of foreign exchange dealers may affect exchange-rate dynamics. According to empirical observations, market makers set exchange rates not only with respect to excess demand but also in recognition of their inventory. Within our model, market makers control their positions by quoting exchange rates that provoke offsetting orders of technical and fundamental traders. Our model demonstrates that such behaviour may amplify trading volume, exchange-rate volatility and deviations from fundamentals.
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A number of recent empirical studies cast some doubt on the random walk theory of asset prices and suggest these display significant transitory components and complex chaotic motion. This paper analyses a model of fundamentalists and chartists which can generate a number of dynamic regimes which are compatible with the recent empirical evidence.
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This paper examines a nonlinear disequilibrium model of price formation in speculative markets with two groups of speculators, fundamentalists and chartists. The behavior of the fundamentalists is stabilizing, whereas that of the chartists is destabilizing; a sufficiently high share of wealth in the hands of the latter group can cause attracting periodic orbits to arise. If information about fundamentals is costly to obtain, then chartists obtain higher pay-offs in a stable regime, while fundamentalists perform better in an unstable regime. This gives rise to endogenous regime switching: the market alternates between periods of stability and instability, with the transition from one regime to another determined endogenously through the evolution of wealth shares.
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We investigate asset pricing dynamics in an adaptive evolutionary asset pricing model with fundamentalists, trend followers and a market maker. Agents can choose between a fundamentalist strategy at positive information cost or choose a trend following strategy for free. Price adjustment is proportional to the excess demand in the asset market. Agents asynchronously update their strategy according to realized net profits in the recent past. As agents become more sensitive to differences in strategy performance, the fundamental steady state becomes unstable and multiple steady states may arise. As the traders’ sensitivity to differences in fitness increases, a bifurcation route to chaos sets in due to homoclinic bifurcations of stable and unstable manifolds of the fundamental steady state.
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A deterministic trading strategy can be regarded as a signal processing element that uses external information and past prices as inputs and incorporates them into future prices. This paper uses a market maker based method of price formation to study the price dynamics induced by several commonly used financial trading strategies, showing how they amplify noise, induce structure in prices, and cause phenomena such as excess and clustered volatility.
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This chapter surveys work on dynamic heterogeneous agent models (HAMs) in economics and finance. Emphasis is given to simple models that, at least to some extent, are tractable by analytic methods in combination with computational tools. Most of these models are behavioral models with boundedly rational agents using different heuristics or rule of thumb strategies that may not be perfect, but perform reasonably well. Typically these models are highly nonlinear, e.g. due to evolutionary switching between strategies, and exhibit a wide range of dynamical behavior ranging from a unique stable steady state to complex, chaotic dynamics. Aggregation of simple interactions at the micro level may generate sophisticated structure at the macro level. Simple HAMs can explain important observed stylized facts in financial time series, such as excess volatility, high trading volume, temporary bubbles and trend following, sudden crashes and mean reversion, clustered volatility and fat tails in the returns distribution.
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This paper analyses the dynamics of a model of a share market consisting of two groups of traders: fundamentalists, who base their trading decisions on the expectation of a return to the fundamental value of the asset, and chartists, who base their trading decisions on an analysis of past price trends. The model is reduced to a two-dimensional map whose global dynamic behaviour is analysed in detail. The dynamics are affected by parameters measuring the strength of fundamentalist demand and the speed with which chartists adjust their estimate of the trend to past price changes. The parameter space is characterized according to the local stability/instability of the equilibrium point as well as the non-invertibility of the map. The method of critical curves of non-invertible maps is used to understand and describe the range of global bifurcations that can occur. It is also shown how the knowledge of deterministic dynamics uncovered here can aid in understanding the behaviour of stochastic versions of the model.
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This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their ‘beliefs’ in each period in a boundedly rational way, according to a ‘fitness measure’ such as past realized profits. Price fluctuations are thus driven by an evolutionary dynamics between different expectation schemes (‘rational animal spirits’). Using a mixture of local bifurcation theory and numerical methods, we investigate possible bifurcation routes to complicated asset price dynamics. In particular, we present numerical evidence of strange, chaotic attractors when the intensity of choice to switch prediction strategies is high.
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By studying two well known hypotheses in economics, this paper illustrates how emergent properties can be shown in an agent-based artificial stock market. The two hypotheses considered are the efficient market hypothesis and the rational expectations hypothesis. We inquire whether the macrobehavior depicted by these two hypotheses is consistent with our understanding of the microbehavior. In this agent-based model, genetic programming is applied to evolving a population of traders learning over time. We first apply a series of econometric tests to show that the EMH and the REH can be satisfied with some portions of the artificial time series. Then, by analyzing traders’ behavior, we show that these aggregate results cannot be interpreted as a simple scaling-up of individual behavior. A conjecture based on sunspot-like signals is proposed to explain why macrobehavior can be very different from microbehavior. We assert that the huge search space attributable to genetic programming can induce sunspot-like signals, and we use simulated evolved complexity of forecasting rules and Granger causality tests to examine this assertion.
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We propose a model with heterogeneous interacting traders which can explain some of the stylized facts of stock market returns. In the model, synchronization effects, which generate large fluctuations in returns, can arise purely from communication and imitation among traders. The key element in the model is the introduction of a trade friction which, by responding to price movements, creates a feedback mechanism on future trading and generates volatility clustering. The model also reproduces the empirically observed positive cross-correlation between volatility and trading volume.
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A deterministic excess demand model of stock market behavior is presented that generates stochastically fluctuating prices and randomly switching bear and bull markets.
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We present a behavioral stock market model in which traders are driven by greed and fear. In general, the agents optimistically believe in rising markets and thus buy stocks. But if stock prices change too abruptly, they panic and sell stocks. Our model mimics some stylized facts of stock market dynamics: (1) stock prices increase over time, (2) stock markets sometimes crash, (3) stock prices show little pair correlation between successive daily changes, and (4) periods of low volatility alternate with periods of high volatility. A strong feature of the model is that stock prices completely evolve according to a deterministic low-dimensional nonlinear law of motion.
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This article highlights several issues from simulating agent-based financial markets. These all center around the issue of learning in a multiagent setting, and specifically the question of whether the trading behavior of short-memory agents could interfere with the learning process of the market as whole. It is shown in a simple example that short-memory traders persist in generating excess volatility and other features common to actual markets. Problems related to short-memory trader behavior can be eliminated by using several different methods. These are discussed along with their relevance to agent-based models in general.
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This paper develops a model of market making that incorporates both inventory control and asymmetric information effects. We show that the specialist acts both as a market maker and as an active investor trading for his own account. As a market maker, the specialist quotes prices that induce mean reversion toward a desired level of inventory; as an active investor, he periodically adjusts the target inventory levels towards which inventories revert. We test the model using data obtained from a NYSE specialist. We find that specialist inventories exhibit mean reversion, but the adjustment process is slow, even controlling for shifts in target inventories. The model also predicts that quote revisions are negatively related to specialist trades and positively related to the information conveyed by order imbalances. We find strong evidence for this hypothesis; further, our results suggest that specialist quotes anticipate future order imbalances.
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Optimal pricing strategies have been proposed by many authors for security exchange specialists. Successful application of these algorithms requires specialists to behave as if they knew the equilibrium strategy for a complicated dynamic game. Real life security exchange specialists actually use relatively simpler price adjustment rules. The current paper carries out an economic analysis of one of these rules. The analysis suggests that to make a viable market the specialist has to churn the market, and to behave optimally he may have to sacrifice his affirmative obligation to maintain “a fair and orderly market.” The analysis also suggests that the direct tick test is not an adequate test of the specialist's affirmative obligation. A more comprehensive test should include the test of price adjustment speed.
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This paper examines the empirical relationship between 20 minute trading volume and price quotes announced by market makers for a sample of liquid stocks on the London Stock Exchange, over a settlement period in 1990. We outline a simple model which highlights three key players in the market: market makers, informed traders and liquidity traders. We determine the optimal prices that a market maker will quote as a function of the expected fundamental price, the expected number of liquidity trades and the lagged level of inventories. We then go on to analyse the empirical implications of this model, estimate the model's parameters using data provided by the London Stock Exchange and test the restrictions implied by our theory. The analysis yields tests for the existence of asymmetric information, stock control and liquidity trade effects on price quote revisions. We find little evidence of asymmetric information for our sample, but strong inventory control effects.
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Using London Stock Exchange data, we test the central implication of the canonical model of Ho and Stoll (1983) that relative inventory differences determine dealer behavior. We find that relative inventories explain which dealers obtain large trades and show that movements between best ask, best bid, and straddle are highly correlated with both standardized and relative inventory changes. We show that the mean reversion in inventories is highly nonlinear and increasing in inventory levels. We show that a key determinant of variations in interdealer trading is inventories and that interdealer trading plays an important role in managing large inventory positions. Copyright The American Finance Association 1998.
Article
The authors develop a dynamic model of market-making incorporating inventory and information effects. The marketmaker is both a dealer and an investor, quoting prices that induce mean reversion in inventory toward targets determined by portfolio considerations. The authors test the model with inventory data from a New York Stock Exchange specialist. Specialist inventories exhibit slow mean reversion, with a half-life of over forty-nine days, suggesting weak inventory effects. However, after controlling for shifts in desired inventories, the half-life falls to seven and three-tenths days. Further, quote revisions are negatively related to specialist trades and are positively related to the information conveyed by order imbalances. Copyright 1993 by American Finance Association.
Article
This paper attempts to formalize herd behavior or mutual mimetic contagion in speculative markets. The emergence of bubbles is explained as a self-organizing process of infection among traders leading to equilibrium prices which deviate from fundamental values. It is postulated furthermore that the speculators' readiness to follow the crowd depends on one basic economic variable, namely actual returns. Above average returns are reflected in a generally more optimistic attitude that fosters the disposition to overtake others' bullish beliefs and vice versa. This economic influence makes bubbles transient phenomena and leads to repeated fluctuations around fundamental values. Copyright 1995 by Royal Economic Society.
Article
We identify incentives generated by the Bretton Woods II system that may have contributed to the sub-prime liquidity crisis now working its way through the international monetary system. We then evaluate the persistent conjecture that the liquidity crisis is or will become a balance of payments crisis for the United States. Given that it happens, the additional costs associated with a sudden stop of net capital flows to the United States could be quite substantial. But we observe that emerging market governments have continued to acquire US assets even as yields have fallen, and the incentives for continuing to do so remain strong. Moreover, the Bretton Woods II system, which has clearly been the most resilient of the forces driving current markets, continues to generate low real interest rates in industrial countries and growth in emerging markets that will help limit the damage from the liquidity crisis. Copyright © 2009 Blackwell Publishing Ltd.
Article
This paper presents a transaction-level empirical analysis of the trading activities of New York Stock Exchange specialists. The main findings of the analysis are the following: adjustment lags in inventories vary across stocks and are in some cases as long as one or two months; decomposition of specialist trading profits by trading horizon shows that the principal source of these profits is short term; an analysis of the dynamic relations among inventories, signed order flow, and quote changes suggests that trades in which the specialist participates have a higher immediate impact on the quotes than trades with no specialist participation. Copyright 1993 by American Finance Association.
Article
Market liquidity is modeled as being determined by the demand and supply of immediacy. Exogenous liquidity events coupled with the risk of delayed trade create a demand for immediacy. Market makers supply immediacy by their continuous presence. and willingness to bear risk during the time period between the arrival of final buyers and sellers. In the long run the number of market makers adjusts to equate the supply and demand for immediacy. This determine the equilibrium level of liquidity in the market. The lower is the autocorrelation in rates of return, the higher is the equilibrium level of liquidity.
Article
Satisfied as we may be with the overall efficiency of the market system and with the tenets of the perfect market model, we all viscerally know that were we down on the market floor we would certainly react to a multitude of apparent price discrepancies. Indeed, it is intuitively inconceivable that a man‐made institution (such as the market) could be so mechanically perfect that all such discrepancies would be totally annihilated before they can be observed. Accordingly, we would expect floor traders and other professionals to be speculating abundantly on what they perceive to be the direction in which the market is going. Almost surely, such behavior has an effect on the dynamics of stock prices. A financial theory that cavalierly ignores this component in the determination of prices would be regrettably deficient.