Robot traders can prevent extreme events in complex stock markets

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Abstract

If stock markets are complex, monetary policy and even financial regulation may be useless to prevent bubbles and crashes. Here, we suggest the use of robot traders as an anti-bubble decoy. To make our case, we put forward a new stochastic cellular automata model that generates an emergent stock price dynamics as a result of the interaction between traders. After introducing socially integrated robot traders, the stock price dynamics can be controlled, so as to make the market more Gaussian.

Introduction

The recent crisis caught the economists in a misplaced consensus of “one instrument one target”. The instrument was the nominal interest rate, and the monetary policy focused only on an implicit inflation target. Stock market bubbles were dismissed as unimportant. After the bursting of the subprime housing bubble, the collapse of the theory prompted a rebirth of old-style Keynesianism, along with talks of an elusive “macroprudential” regulation. However, such approaches fail to recognize the basic fact that stock markets are complex systems.

Prior to the financial crisis, on one side of the controversy on whether central banks should respond to stock price movements, Bernanke and Gentler [1] argued that as a central bank was committed to inflation targeting, it was not generally desirable that monetary policy should react to stock price movements (Ref. [2] and references therein for an overview of the debate). This point of view coincided with that of the US Federal Reserve. The Fed thus believed that monetary policy should not preemptively react to an asset bubble that was uncertain and thus difficult to track and “prick”, but it should strongly react after the bubble had burst. After the deep recession in the aftermath of the crash, the Fed seems to have abandoned this perspective. However, there is still a vacuum in theory about the modus operandi of financial regulation.

The main problem here is that the regulation of a complex system such as the stock market cannot be achieved using conventional policy tools. Although economists are hardly prepared to recognize this fact [3], here one has to resort to the control theory of self-organized systems [4]. Collective behavior based on self-organization has been shown in animals living in groups as well as in humans. This prompted engineers to devise autonomous robots that relied on self-organization as a main coordination mechanism. The controller of individual robots is designed using reactive, behavior-based techniques. Socially integrated autonomous robots, perceived as congeners by the group, and acting as interactive decoys will be able to control self-organized choices [5].

Self-organization is a feature of complex stock markets [6], [7], and robot trading is ubiquitous. We take these facts into account to make a case for the robots to counteract the imitative behavior of human traders, which occasionally leads to bubbles. If correctly engineered, this offers an alternative to monetary policy and conventional regulation, to stabilize stock markets.

Simple software-based traders have been around for many years (some even blamed the first generation of robots for the crash of 1987 [8]), but they are now becoming far more sophisticated, and make trades worth tens of billions of dollars every day. They already appear to be outperforming their human counterparts in the equity markets, where they are buying and selling shares. It is almost impossible for an exchange to tell whether a person or an algorithm is issuing trades. Under such circumstances, why not use the robot traders as an anti-bubble decoy?

To show how this can be accomplished, we put forward a new stochastic cellular automata model that generates an emergent stock price dynamics as a result of the interaction between traders. After introducing socially integrated robot traders, the stock price dynamics can be controlled, so as to make the market more Gaussian.

The rest of this article is organized as follows. Section 2 sets up our cellular automata model of the stock market where imitation plays a key role. Section 3 describes the market price dynamics of the model. Through parameter calibration, the model is made empirically relevant by matching its properties with those of the real world stock market, the Sao Paulo Stock Exchange (Bovespa, for short). Section 4 introduces the robot traders into the model, and Section 5 assesses their impact on the stock price dynamics. Section 6 concludes the study.

Section snippets

The model

We set the new stochastic cellular automata model to study the stock price dynamics where the interactions between the market participants play a key role (see also Ref. [9]). Initially, there are only human traders, and subsequently, robot traders enter the market. The traders are represented by cells on a two-dimensional L×L grid. There are N traders who can either buy or sell only one share, and these are two mutually exclusive states. At any given time step t, the population of traders N is

Market price dynamics

As usual, we have considered log returns rather than the prices, that is, R(t)=lnP(t+1)lnP(t), which are standardized, so that they have a zero mean and unit standard deviation. To make our model empirically relevant we have calibrated its three parameters λ, κ, and μ, to match the statistical properties of the log returns of the Bovespa index. For all the experiments below we have set F¯=1. We have considered the daily data of the index from the period July 5, 1994 to June 30, 2009, which

The model with robot traders

We now introduce robot traders into the model. The robots are socially integrated into the group of human traders to control self-organized market returns. We assume that humans and robots are perceived as congeners and influence one another in the same way. Robot behavior is intentionally set to an anti-imitation rule to counteract the imitative human trader behavior as described by Eq. (2). The robots adopt such a contrarian behavior using the majority principle after considering the

Market price dynamics after the introduction of robots

To run the experiments with the robots, we adopted the same setup of the basic model: the structure of the cellular automata and the initial conditions were retained, that is, λ=1, κ=9, and μ=2×1010. However, we still needed to specify how the robot traders are inserted into the market. At the start of each simulation, we randomly distributed a fixed number of robots in the grid. In the initial state, half the robots were buyers and the other half were sellers.

Our findings show that even when

Conclusion

We devised a new stochastic cellular automata model of the stock market and calibrated its key parameters to fit the empirical data properties of an actual stock market, the Bovespa. We showed that its non-Gaussian profile could be replicated by the model.

The imitation rule of the traders was then counteracted with an anti-imitation rule intentionally ascribed to robot traders. The model with robots was able to modulate the collective decision-making process and produce a market pattern not

Acknowledgements

We are grateful to the comments made by four anonymous referees.

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