We present a simple model of a non-equilibrium self-organizing market where asset prices are partially driven by investment decisions of a bounded-rational agent. The agent acts in a stochastic market environment driven by various exogenous "alpha" signals, agent's own actions (via market impact), and noise. Unlike traditional agent-based models, our agent aggregates all traders in the market, rather than being a representative agent. Therefore, it can be identified with a bounded-rational component of the market itself, providing a particular implementation of an Invisible Hand market mechanism. In such setting, market dynamics are modeled as a fictitious self-play of such bounded-rational market-agent in its adversarial stochastic environment. As rewards obtained by such self-playing market agent are not observed from market data, we formulate and solve a simple model of such market dynamics based on a neuroscience-inspired Bounded Rational Information Theoretic Inverse Reinforcement Learning (BRIT-IRL). This results in effective asset price dynamics with a non-linear mean reversion - which in our model is generated dynamically, rather than being postulated. We argue that our model can be used in a similar way to the Black-Litterman model. In particular, it represents, in a simple modeling framework, market views of common predictive signals, market impacts and implied optimal dynamic portfolio allocations, and can be used to assess values of private signals. Moreover, it allows one to quantify a "market-implied" optimal investment strategy, along with a measure of market rationality. Our approach is numerically light, and can be implemented using standard off-the-shelf software such as TensorFlow.
Of course, deficiencies of standard financial models based on competitive market equilibrium and or no-arbitrage paradigm were not left unnoticed both within the financial community, and among researchers in other disciplines, most notably physics and computer science. The latter disciplines contributed a number of interesting and fresh ideas to financial modeling @cite_39 , @cite_8 . In particular, agent-based models may provide interesting insight into how financial markets can operate when viewed as evolving complex systems , see e.g. @cite_12 .
@cite_8 @cite_12 @cite_39
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Chakrabarti.- A discussion on Econophysics by Hideaki Aoyama. A growing body of recent literature allows for heterogenous trading strategies and limited rationality of agents in behavioral models of financial markets. More and more, this literature has been concerned with the explanation of some of the stylized facts of financial markets. It now seems that some previously mysterious time-series characteristics like fat tails of returns and temporal dependence of volatility can be observed in many of these models as macroscopic patterns resulting from the interaction among different groups of speculative traders. However, most of the available evidence stems from simulation studies of relatively complicated models which do not allow for analytical solutions. In this paper, this line of research is supplemented by analytical solutions of a simple variant of the seminal herding model introduced by Kirman [1993]. Embedding the herding framework into a simple equilibrium asset pricing model, we are able to derive closed-form solutions for the time-variation of higher moments as well as related quantities of interest enabling us to spell out under what circumstances the model gives rise to realistic behavior of the resulting time series Given the economy's complex behavior and sudden transitions as evidenced in the 2007–08 crisis, agent-based models are widely considered a promising alternative to current macroeconomic practice dominated by DSGE models. Their failure is commonly interpreted as a failure to incorporate heterogeneous interacting agents. This paper explains that complex behavior and sudden transitions also arise from the economy's financial structure as reflected in its balance sheets, not just from heterogeneous interacting agents. It introduces "flow-of-funds" and "accounting" models, which were preeminent in successful anticipations of the recent crisis. In illustration, a simple balance-sheet model of the economy is developed to demonstrate that nonlinear behavior and sudden transition may arise from the economy’s balance-sheet structure, even without any microfoundations. The paper concludes by discussing one recent example of combining flow-of-funds and agent-based models. This appears a promising avenue for future research. We introduce a minimal Agent Based Model for financial markets to understand the nature and Self-Organization of the Stylized Facts. The model is minimal in the sense that we try to identify the essential ingredients to reproduce the main most important deviations of price time series from a Random Walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The Stylized Facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effect which, however, can occur at different time scales. We propose a new mechanism for the Self-Organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represent a crucial element for this state of Self-Organized-Intermittency. The model can be easily generalized to consider more realistic variants.