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arXiv2019

Stock market microstructure inference via multi-agent reinforcement learning

Quantitative finance has had a long tradition of a bottom-up approach to complex systems inference via multi-agent systems (MAS). These statistical tools are based on modelling agents trading via a centralised order book, in order to emulate complex and diverse market phenomena. These past financial models have all relied on so-called zero-intelligence agents, so that the crucial issues of agent information and learning, central to price formation and hence to all market activity, could not be properly assessed. In order to address this, we designed a next-generation MAS stock market simulator, in which each agent learns to trade autonomously via model-free reinforcement learning. We calibrate the model to real market data from the London Stock Exchange over the years $2007$ to $2018$, and show that it can faithfully reproduce key market microstructure metrics, such as various price autocorrelation scalars over multiple time intervals. Agent learning thus enables model emulation of the microstructure with greater realism.

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arXiv2020

Strategic Formation and Reliability of Supply Chain Networks

Supply chains are the backbone of the global economy. Disruptions to them can be costly. Centrally managed supply chains invest in ensuring their resilience. Decentralized supply chains, however, must rely upon the self-interest of their individual components to maintain the resilience of the entire chain. We examine the incentives that independent self-interested agents have in forming a resilient supply chain network in the face of production disruptions and competition. In our model, competing suppliers are subject to yield uncertainty (they deliver less than ordered) and congestion (lead time uncertainty or, "soft" supply caps). Competing retailers must decide which suppliers to link to based on both price and reliability. In the presence of yield uncertainty only, the resulting supply chain networks are sparse. Retailers concentrate their links on a single supplier, counter to the idea that they should mitigate yield uncertainty by diversifying their supply base. This happens because retailers benefit from supply variance. It suggests that competition will amplify output uncertainty. When congestion is included as well, the resulting networks are denser and resemble the bipartite expander graphs that have been proposed in the supply chain literature, thereby, providing the first example of endogenous formation of resilient supply chain networks, without resilience being explicitly encoded in payoffs. Finally, we show that a supplier's investments in improved yield can make it worse off. This happens because high production output saturates the market, which, in turn lowers prices and profits for participants.

cs.GT↗

arXiv2019

How to design a derivatives market?

We consider the problem of designing a derivatives exchange aiming at addressing clients needs in terms of listed options and providing suitable liquidity. We proceed into two steps. First we use a quantization method to select the options that should be displayed by the exchange. Then, using a principal-agent approach, we design a make take fees contract between the exchange and the market maker. The role of this contract is to provide incentives to the market maker so that he offers small spreads for the whole range of listed options, hence attracting transactions and meeting the commercial requirements of the exchange.

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arXiv2019

CME Iceberg Order Detection and Prediction

We propose a method for detection and prediction of native and synthetic iceberg orders on Chicago Mercantile Exchange. Native (managed by the exchange) icebergs are detected using discrepancies between the resting volume of an order and the actual trade size as indicated by trade summary messages, as well as by tracking order modifications that follow trade events. Synthetic (managed by market participants) icebergs are detected by observing limit orders arriving within a short time frame after a trade. The obtained icebergs are then used to train a model based on the Kaplan--Meier estimator, accounting for orders that were cancelled after a partial execution. The model is utilized to predict the total size of newly detected icebergs. Out of sample validation is performed on the full order depth data, performance metrics and quantitative estimates of hidden volume are presented.

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arXiv2020

Mechanics of good trade execution in the framework of linear temporary market impact

We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to the actual realisation of the traded asset price path over the trading period; this is paramount in volatile regimes, where price trajectories can considerably deviate from their expected value. Remarkably however, the implementation of our strategies does not require the full specification of an SDE evolution for the traded asset price, making them robust across different models. Moreover, rather than minimising the expected trading cost, good trade execution strategies minimise trading costs in a pathwise sense, a point of view not yet considered in the literature. The mathematical apparatus for such a pathwise minimisation hinges on certain random Young differential equations that correspond to the Euler-Lagrange equations of the classical Calculus of Variations. These Young differential equations characterise our good trade execution strategies in terms of an initial value problem that allows for easy implementations.

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arXiv2019

Explaining Agent-Based Financial Market Simulation

This paper is intended to explain, in simple terms, some of the mechanisms and agents common to multiagent financial market simulations. We first discuss the necessity to include an exogenous price time series ("the fundamental value") for each asset and three methods for generating that series. We then illustrate one process by which a Bayesian agent may receive limited observations of the fundamental series and estimate its current and future values. Finally, we present two such agents widely examined in the literature, the Zero Intelligence agent and the Heuristic Belief Learning agent, which implement different approaches to order placement.

cs.MA↗

arXiv2019

A Cloud-Native Globally Distributed Financial Exchange Simulator for Studying Real-World Trading-Latency Issues at Planetary Scale

We describe a new public-domain open-source simulator of an electronic financial exchange, and of the traders that interact with the exchange, which is a truly distributed and cloud-native system that been designed to run on widely available commercial cloud-computing services, and in which various components can be placed in specified geographic regions around the world, thereby enabling the study of planetary-scale latencies in contemporary automated trading systems. Our simulator allows an exchange server to be launched in the cloud, specifying a particular geographic zone for the cloud hosting service; automated-trading clients which attach to the exchange can then also be launched in the cloud, in the same geographic zone and/or in different zones anywhere else on the planet, and those clients are then subject to the real-world latencies introduced by planetary-scale cloud communication interconnections. In this paper we describe the design and implementation of our simulator, called DBSE, which is based on a previous public-domain simulator, extended in ways that are partly inspired by the architecture of the real-world Jane Street Exchange. DBSE relies fundamentally on UDP and TCP network communications protocols and implements a subset of the FIX de facto standard protocol for financial information exchange. We show results from an example in which the exchange server is remotely launched on a cloud facility located in London (UK), with trader clients running in Ohio (USA) and Sydney (Australia). We close with discussion of how our simulator could be further used to study planetary-scale latency arbitrage in financial markets.

cs.CY↗

arXiv2019

Libra: Fair Order-Matching for Electronic Financial Exchanges

While historically, economists have been primarily occupied with analyzing the behaviour of the markets, electronic trading gave rise to a new class of unprecedented problems associated with market fairness, transparency and manipulation. These problems stem from technical shortcomings that are not accounted for in the simple conceptual models used for theoretical market analysis. They, thus, call for more pragmatic market design methodologies that consider the various infrastructure complexities and their potential impact on the market procedures. First, we formally define temporal fairness and then explain why it is very difficult for order-matching policies to ensure it in continuous markets. Subsequently, we introduce a list of system requirements and evaluate existing "fair" market designs in various practical and adversarial scenarios. We conclude that they fail to retain their properties in the presence of infrastructure inefficiencies and sophisticated technical manipulation attacks. Based on these findings, we then introduce Libra, a "fair" policy that is resilient to gaming and tolerant of technical complications. Our security analysis shows that it is significantly more robust than existing designs, while Libra's deployment (in a live foreign currency exchange) validated both its considerably low impact on the operation of the market and its ability to reduce speed-based predatory trading.

cs.CR↗

arXiv2019

Do speed bumps curb low-latency trading? Evidence from a laboratory market

Exchanges implement intentional trade delays to limit the harmful impact of low-latency trading. Do such "speed bumps" curb investment in fast trading technology? Data is scarce since trading technologies are proprietary. We build an experimental trading platform where participants face speed bumps and can invest in fast trading technology. We find that asymmetric speed bumps, on average, reduce investment in speed by only 20%. Increasing the magnitude of the speed bump by one standard deviation further reduces low-latency investment by 8.33%. Finally, introducing a symmetric speed bump leads to the same investment level as no speed bump at all.

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arXiv2019

How Option Hedging Shapes Market Impact

We present a perturbation theory of the market impact based on an extension of the framework proposed by [Loeper, 2018] -- originally based on [Liu and Yong, 2005] -- in which we consider only local linear market impact. We study the execution process of hedging derivatives and show how these hedging metaorders can explain some stylized facts observed in the empirical market impact literature. As we are interested in the execution process of hedging we will establish that the arbitrage opportunities that exist in the discrete time setting vanish when the trading frequency goes to infinity letting us to derive a pricing equation. Furthermore our approach retrieves several results already established in the option pricing literature such that the spot dynamics modified by the market impact. We also study the relaxation of our hedging metaorders based on the fair pricing hypothesis and establish a relation between the immediate impact and the permanent impact which is in agreement with recent empirical studies on the subject.

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arXiv2019

Stock price formation: useful insights from a multi-agent reinforcement learning model

In the past, financial stock markets have been studied with previous generations of multi-agent systems (MAS) that relied on zero-intelligence agents, and often the necessity to implement so-called noise traders to sub-optimally emulate price formation processes. However recent advances in the fields of neuroscience and machine learning have overall brought the possibility for new tools to the bottom-up statistical inference of complex systems. Most importantly, such tools allows for studying new fields, such as agent learning, which in finance is central to information and stock price estimation. We present here the results of a new generation MAS stock market simulator, where each agent autonomously learns to do price forecasting and stock trading via model-free reinforcement learning, and where the collective behaviour of all agents decisions to trade feed a centralised double-auction limit order book, emulating price and volume microstructures. We study here what such agents learn in detail, and how heterogenous are the policies they develop over time. We also show how the agents learning rates, and their propensity to be chartist or fundamentalist impacts the overall market stability and agent individual performance. We conclude with a study on the impact of agent information via random trading.

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arXiv2023

Singular Perturbation Expansion for Utility Maximization with Order-$ε$ Quadratic Transaction Costs

We present an expansion for portfolio optimization in the presence of small, instantaneous, quadratic transaction costs. Specifically, the magnitude of transaction costs has a coefficient that is of the order $ε$ small, which leads to the optimization problem having an asymptotically-singular Hamilton-Jacobi-Bellman equation whose solution can be expanded in powers of $\sqrtε$. In this paper we derive explicit formulae for the first two terms of this expansion. Analysis and simulation are provided to show the behavior of this approximating solution.

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arXiv2021

Stochastic leverage effect in high-frequency data: a Fourier based analysis

The stochastic leverage effect, defined as the standardized covariation between the returns and their related volatility, is analyzed in a stochastic volatility model set-up. A novel estimator of the effect is defined using a pre-estimation of the Fourier coefficients of the return and the volatility processes. The consistency of the estimator is proven. Moreover, its finite sample properties are studied in the presence of microstructure noise effects. The Fourier methodology is applied to S\&P500 futures prices to investigate the magnitude of the stochastic leverage effect detectable at high-frequency.

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arXiv2020

Conservation Laws in a Limit Order Book

We present a class of macroscopic models of the Limit Order Book to simulate the aggregate behaviour of market makers in response to trading flows. The resulting models are solved numerically and asymptotically, and a class of similarity solutions linked to order book formation and recovery is explored. The main result is that order book recovery from aggressive liquidity taking follows a simple $t^{1/3}$ scaling law.

q-fin.TR↗

arXiv2019

Adaptive-Aggressive Traders Don't Dominate

For more than a decade Vytelingum's Adaptive-Aggressive (AA) algorithm has been recognized as the best-performing automated auction-market trading-agent strategy currently known in the AI/Agents literature; in this paper, we demonstrate that it is in fact routinely outperformed by another algorithm when exhaustively tested across a sufficiently wide range of market scenarios. The novel step taken here is to use large-scale compute facilities to brute-force exhaustively evaluate AA in a variety of market environments based on those used for testing it in the original publications. Our results show that even in these simple environments AA is consistently out-performed by IBM's GDX algorithm, first published in 2002. We summarize here results from more than one million market simulation experiments, orders of magnitude more testing than was reported in the original publications that first introduced AA. A 2019 ICAART paper by Cliff claimed that AA's failings were revealed by testing it in more realistic experiments, with conditions closer to those found in real financial markets, but here we demonstrate that even in the simple experiment conditions that were used in the original AA papers, exhaustive testing shows AA to be outperformed by GDX. We close this paper with a discussion of the methodological implications of our work: any results from previous papers where any one trading algorithm is claimed to be superior to others on the basis of only a few thousand trials are probably best treated with some suspicion now. The rise of cloud computing means that the compute-power necessary to subject trading algorithms to millions of trials over a wide range of conditions is readily available at reasonable cost: we should make use of this; exhaustive testing such as is shown here should be the norm in future evaluations and comparisons of new trading algorithms.

q-fin.TR↗

arXiv2019

Fragmentation of Distributed Exchanges

Distributed securities exchanges may become de facto fragmented if they span geographical regions with asymmetric computer infrastructure. First, we build an economic model of a decentralized exchange with two miner clusters, standing in for compact areas of economic activity (e.g., cities). "Local" miners in the area with relatively higher trading activity only join a decentralized exchange if they enjoy a large speed advantage over "long-distance" competitors. This is due to a transfer of economic value across miners, specifically from high- to low-activity clusters. Second, we estimate the speed advantage of "local" over "long-distance" miners in a series of Monte Carlo experiments over a two-cluster, unstructured peer-to-peer network simulated in C. We find that the speed advantage increases in the level of infrastructure asymmetry between clusters. Cross-region DEX blockchains are feasible as long as the asymmetry levels in trading activity and infrastructure availability across regions are positively correlated.

q-fin.TR↗

arXiv2019

Deep reinforcement learning for market making in corporate bonds: beating the curse of dimensionality

In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for a large number of bonds to asset managers from all around the globe. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. Useful models exist, most of them inspired by that of Avellaneda and Stoikov. These models describe the complex optimization problem faced by market makers: proposing bid and ask prices in an optimal way for making money out of the difference between bid and ask prices while mitigating the market risk associated with holding inventory. While most of the models only tackle one-asset market making, they can often be generalized to a multi-asset framework. However, the problem of solving numerically the equations characterizing the optimal bid and ask quotes is seldom tackled in the literature, especially in high dimension. In this paper, our goal is to propose a numerical method for approximating the optimal bid and ask quotes over a large universe of bonds in a model à la Avellaneda-Stoikov. Because we aim at considering a large universe of bonds, classical finite difference methods as those discussed in the literature cannot be used and we present therefore a discrete-time method inspired by reinforcement learning techniques. More precisely, the approach we propose is a model-based actor-critic-like algorithm involving deep neural networks.

q-fin.CP↗

arXiv2019

From microscopic price dynamics to multidimensional rough volatility models

Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried out in the mono-asset case. In this work, we show that some specific multivariate rough volatility models arise naturally from microstructural properties of the joint dynamics of asset prices. To do so, we use Hawkes processes to build microscopic models that reproduce accurately high frequency cross-asset interactions and investigate their long term scaling limits. We emphasize the relevance of our approach by providing insights on the role of microscopic features such as momentum and mean-reversion on the multidimensional price formation process. We in particular recover classical properties of high-dimensional stock correlation matrices.

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