Methods for Calibrating Agent-Based Market Simulators

Table of Links

Abstract and 1. Introduction

2. Relevant Work

3. Methods

3.1 Models

3.2 Summarising Features

3.3 Calibration of Market Model Parameters

4. Experiments

4.1 Zero Intelligence Trader

4.2 Extended Chiarella

4.3 Historical Data

5. Discussion & Future Work

6. Significance, Acknowledgments, and References

3 METHODS

In this work, we show how simulation-based inference can be used to calibrate an ABM market simulator. We demonstrate our approach using two ABMs, a simple model containing a set of zero-intelligence traders, which we refer to as the ZI model, and an extension to the Chiarella model [30], which we refer to as the extended Chiarella model. These models are described in subsection 3.1. Most calibration methods for market simulators use a collection of summary features known in economics and finance as stylised facts [36, 41, 42]. The stylised facts represent commonly observed features generated by market exchanges. In this work, we use stylised facts as an evaluation measure for our calibration framework and instead use the time-series data directly to train our calibration networks. We describe these summarising features as well as the stylised facts used in subsection 3.2. Having outlined both models and summary statistics, we next describe our method for calibration in subsection 3.3. We use neural posterior estimation (NPE) to estimate the posterior probability distribution of parameter sets, conditioned on an observation. To do so, we use two different types of normalising flows, neural spline flows (NSF) and masked auto-regressive flows (MAFs) to approximate the posterior without requiring the likelihood to be calculated. In order to reduce the dimensions of the summary data, we use an embedding network to transform the data into a low-dimensional feature space. Here, we use a simple multi-layer perceptron (MLP) model as our embedding network. However, as we discuss in section 5, other more complex neural network architectures could also act as an effective embedding networks. This is especially true for architectures that match the inductive biases inherent to market dynamics such as a recurrent or graph neural network.