Calibrating emergent phenomena in stock markets with agent based models.

Lucas Fievet,Didier Sornette

doi:10.1371/journal.pone.0193290

Abstract

Since the 2008 financial crisis, agent-based models (ABMs), which account for out-of-equilibrium dynamics, heterogeneous preferences, time horizons and strategies, have often been envisioned as the new frontier that could revolutionise and displace the more standard models and tools in economics. However, their adoption and generalisation is drastically hindered by the absence of general reliable operational calibration methods. Here, we start with a different calibration angle that qualifies an ABM for its ability to achieve abnormal trading performance with respect to the buy-and-hold strategy when fed with real financial data. Starting from the common definition of standard minority and majority agents with binary strategies, we prove their equivalence to optimal decision trees. This efficient representation allows us to exhaustively test all meaningful single agent models for their potential anomalous investment performance, which we apply to the NASDAQ Composite index over the last 20 years. We uncover large significant predictive power, with anomalous Sharpe ratio and directional accuracy, in particular during the dotcom bubble and crash and the 2008 financial crisis. A principal component analysis reveals transient convergence between the anomalous minority and majority models. A novel combination of the optimal single-agent models of both classes into a two-agents model leads to remarkable superior investment performance, especially during the periods of bubbles and crashes. Our design opens the field of ABMs to construct novel types of advanced warning systems of market crises, based on the emergent collective intelligence of ABMs built on carefully designed optimal decision trees that can be reversed engineered from real financial data.

Highlights

Starting from the common definition of standard minority and majority agents with binary strategies, we prove their equivalence to optimal decision trees
Complementary to the influential dynamic stochastic general equilibrium modeling in macroeconomics, agent-based models (ABMs) are suitable to account for bounded rationality and adaptiveness of interacting agents [1,2,3], as well as out-of-equilibrium phenomena
Building on minority and majority ABMs derived from the El Farol Bar problem [9], a number of promising results have been obtained for this class of ABMs: (i) mixed game models with minority and majority agents exhibit trends and bubbles [10, 11]; (ii) majority agents with a delayed action have been found to be crucial for the existence of transitions between herding and contrarian regimes [12]; (iii) significant out-of-sample predictive power on hourly Forex data seems to be present [13]; (iv) predictability has been found to increase prior to large changes [14]; (v) pockets of predictability have been documented when the agents’ actions decouple from past returns [15]; and (vi) significant directional accuracy can be obtained with a single agent model [16, 17]

Summary

Introduction

Complementary to the influential dynamic stochastic general equilibrium modeling in macroeconomics, agent-based models (ABMs) are suitable to account for bounded rationality and adaptiveness of interacting agents [1,2,3], as well as out-of-equilibrium phenomena. Calibrating emergent phenomena in stock markets with agent based models criterion to detect truly predictive models This approach allows us to compare structurally different models, to the Markov information criterion [24]. These two steps prepare the ground for constructing and exploring two-agent models with heterogenous investment horizons, decision processes (games) and decision lags. A delayed strategy s forecasts the direction of the return d steps ahead as ~rtþdþ1 1⁄4 sð~rtÞ, where d is the delay parameter This is a simple way to represent the lag between analysis, decision and action that is often imposed by operational constraints in real-world strategy implementations. The performance U of a strategy s at time t, for the payoff function π, with a delay d, on the past window of size L, is given by

X tÀ 1À d

Motivation

Experiments

Findings

Conclusion