Learning to simulate realistic limit order book markets from data as a World Agent

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Learning to simulate realistic limit order book markets from

data as a World Agent

Andrea Coletta

andrea.coletta@jpmchase.com

J.P. Morgan AI Research

New York, USA

Aymeric Moulin∗

amoulin@bamfunds.com

Balyasny Asset Management, L.P.

New York, USA

Svitlana Vyetrenko

svitlana.s.vyetrenko@jpmchase.com

J.P. Morgan AI Research

New York, USA

Tucker Balch

tucker.balch@jpmchase.com

J.P. Morgan AI Research

New York, USA

ABSTRACT

Multi-agent market simulators usually require careful calibration

to emulate real markets, which includes the number and the type

of agents. Poorly calibrated simulators can lead to misleading con-

clusions, potentially causing severe loss when employed by invest-

ment banks, hedge funds, and traders to study and evaluate trading

strategies. In this paper, we propose a world model simulator that

accurately emulates a limit order book market – it requires no agent

calibration but rather learns the simulated market behavior directly

from historical data. Traditional approaches fail short to learn and

calibrate trader population, as historical labeled data with details

on each individual trader strategy is not publicly available. Our

approach proposes to learn a unique "world" agent from historical

data. It is intended to emulate the overall trader population, without

the need of making assumptions about individual market agent

strategies. We implement our world agent simulator models as a

Conditional Generative Adversarial Network (CGAN), as well as a

mixture of parametric distributions, and we compare our models

against previous work. Qualitatively and quantitatively, we show

that the proposed approaches consistently outperform previous

work, providing more realism and responsiveness.

KEYWORDS

GANs, synthetic data, time-series, nancial markets

ACM Reference Format:

Andrea Coletta, Aymeric Moulin, Svitlana Vyetrenko, and Tucker Balch.

2022. Learning to simulate realistic limit order book markets from data as a

World Agent. In 3rd ACM International Conference on AI in Finance (ICAIF

’22), November 2–4, 2022, New York, NY, USA. ACM, New York, NY, USA,

9 pages. https://doi.org/10.1145/3533271.3561753

∗

The research work was carried out when Aymeric Moulin was employed at J.P. Morgan

AI Research.

Permission to make digital or hard copies of all or part of this work for personal or

classroom use is granted without fee provided that copies are not made or distributed

for prot or commercial advantage and that copies bear this notice and the full citation

on the rst page. Copyrights for components of this work owned by others than the

author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or

republish, to post on servers or to redistribute to lists, requires prior specic permission

and/or a fee. Request permissions from permissions@acm.org.

ICAIF ’22, November 2–4, 2022, New York, NY, USA

ACM ISBN 978-1-4503-9376-8/22/10. . . $15.00

https://doi.org/10.1145/3533271.3561753

(A)

(B)

Figure 1: World Model (A) vs Multi-Agent (B) Simulator.

1 INTRODUCTION

Financial markets are among the most complex systems in exis-

tence. Naturally described as multi-agent systems, they comprise

thousands of interacting heterogeneous participants. Nowadays,

both researchers and traders heavily rely on articial market mod-

els, to support the design of algorithms, as well as testing novel

trading strategies. Articial market models can help to isolate and

study the impact of new algorithms to the price and volume of

the stocks [

]; they can explain the nature of some rare nancial

market phenomena, such as bubbles and crashes [

]; or they can

just be used to study and test trading strategies, before approaching

the real market [6].

Previous work mostly focuses on multi-agent modeling, which is

a natural bottom-up approach to emulate nancial markets [

]. In

these models, a number of decision-makers (agents or traders) and

institutions, interact through prescribed rules to build the market.

Several multi-agent simulators have been developed, by traders

and researchers [

]. However, modeling a realistic market

through a multi-agent simulation is still a major challenge [

In fact, specifying how the agents should behave and interact in

the simulation is not obvious. While some agents can be modeled

following a common sense or historical analysis [

], in general

market participants adopt unknown proprietary trading strategies.

Moreover, public available historical data does not include attribu-

tion to the various market participants, which makes the calibration

of the agents challenging.

To overcome this challenge, learning to simulate from the data

as a world model was introduced in [

]. This approach assumed a

arXiv:2210.09897v1 [q-fin.TR] 26 Sep 2022

ICAIF ’22, November 2–4, 2022, New York, NY, USA Colea et al.

Figure 2: Order book denitions

unique agent trained as a conditional generative adversarial Net-

work (CGAN) [

] from historical data, without the need of making

assumptions about the individual market agent strategies.

The world agent was simplistic: it was only capable of placing limit

orders which usually account for just 50% of all trading actions.

Nevertheless, it was shown in [

] that this model could reproduce

stylized facts as well as some form of market impact of trading -

hence, this work provides a rst attempt to a realistic and respon-

sive world model. Figure 1 shows a classic multi-agent simulator

compared to the World Model, in which all the background agents

are represented with a unique World Agent.

In this paper, we improve the design of the CGAN-based world

model by extending it to support all main market actions (i.e., mar-

ket order, add limit order, cancel order, and replace order), and we

describe it alongside another world model constructed explicitly as

a mixture of parametric distributions. Moreover, we improve the

CGAN robustness and stability by unrolling the model during the

training.

We demonstrate that both approaches presented in this paper

outperform previous work on world model construction by pro-

viding higher degree of simulation realism. We also emphasize

and experimentally demonstrate that the GAN-based model ap-

plies to dierent heterogeneous stocks, as it does not make explicit

assumptions about the data distributions.

2 BACKGROUND

In this section we introduce the readers to limit order book markets,

with a brief introduction to market structure and mechanisms.

2.1 Limit Order Book (LOB)

Financial markets oer a place for buyers and sellers to meet and

trade on dierent assets. Modern electronic markets, such as NAS-

DAQ, provide ad-hoc message protocols to facilitate trades and pro-

vides real-time information about the market order ow and state.

In particular, the ITCH [

] protocol provides access to anonymized

market data with highest granularity, including all the orders in the

market. The main four fundamental orders are: Market orders,Add

limit orders,Cancel orders, and Replace orders. They respectively

indicate the intention of trading a given amount of shares at any

price; the intention of trading shares at a xed limit price; a cancel-

lation of a previous limit order; and a modication to a previous

limit order (e.g., a change in the price or quantity).

Most equity markets employ a continuous-time double auction

mechanism to handle the stream of orders, and to execute a trans-

action whenever a buyer and seller agree on the price [

]. To store

the supply and demand for each asset, the market exchange uses

an electronic record called limit order book (LOB). The LOB keeps

record of all outstanding limit orders into dierent levels, organized

by price, and it continuously updates them according to incoming

orders. Figure 2 shows a snapshot of a LOB with the available supply

(red bars) and demand (green bars). The rst bars (L1) represent the

rst level, the second bars (L2) the second level, and so on. Each bar

keeps the outstanding orders into a queue structure. An add limit

order to buy will update the existing demand, increasing the queue

size (see Figure 2 light green); while a cancel order will decrease the

queue size, and consequently reduce supply or demand.

2.2 Articial Market properties

Realism.

Evaluating trading strategies against poorly calibrated

market models can lead to poor and misleading conclusions, po-

tentially causing severe loss when we employ these strategies on

real markets. To assess the realism of articial models, researchers

commonly evaluate their ability to reproduce statistical properties

of real markets called stylized facts [

]. For example, as as-

set daily returns usually have fat tail distribution and long-range

dependence, we expected the same properties (or stylized facts)

from articial markets. In Section 5 we show that our approach

outperforms existing work under a wide range of stylized facts. In

particular, we consider auto-correlations,heavy tails distribution,

and long range dependence to evaluate asset return properties. While

we consider order volumes,time to rst ll,depth and market spread

distributions, to evaluate the volumes and order ow. 1

Responsiveness.

Another desirable property of articial market

models is the responsiveness to exogenous trading orders: the model

should emulate the market reaction to new orders, providing a tool

to investigate strategies’ impact on the market. For example, the

arrival of several buy (sell) market orders commonly causes the rise

(fall) of the price. This phenomenon is called price impact, and it

desirable that a responsive model exhibit this behavior.

In section 5 we evaluate the responsiveness of our model by

simulating the arrival of a burst of buy/sell orders [1].

2.3 Generative Models and CGANs

In the last years generative models have been successfully employed

in a wide range of scenarios, ranging from images to time-series.

A generative model is any model able to learn a probability distri-

bution

𝑝model

resembling the real data distribution

𝑝data

, from a

set of real samples. Among generative models, we can identify two

major approaches: a) models that explicitly estimate the probability

density function; b) and models that implicitly learn to generate

samples without the need of an explicit density function [10].

Generative Adversarial Networks (GANs)

.GANs are power-

ful generative models that consider two adversarial neural networks,

which implicitly learn to generate data samples [

]. In particular,

a generator

𝐺

and a discriminator

𝐷

are trained simultaneously to

1We refer the reader to the work in [24] for a detailed introduction to stylized facts.

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LearningtosimulaterealisticlimitorderbookmarketsfromdataasaWorldAgentAndreaColettaandrea.coletta@jpmchase.comJ.P.MorganAIResearchNewYork,USAAymericMoulin∗amoulin@bamfunds.comBalyasnyAssetManagement,L.P.NewYork,USASvitlanaVyetrenkosvitlana.s.vyetrenko@jpmchase.comJ.P.MorganAIResearchNewYork,USATucker...

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Learning to simulate realistic limit order book markets from data as a World Agent

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