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arXiv2018

Supporting Crowd-Powered Science in Economics: FRACTI, a Conceptual Framework for Large-Scale Collaboration and Transparent Investigation in Financial Markets

Modern investigation in economics and in other sciences requires the ability to store, share, and replicate results and methods of experiments that are often multidisciplinary and yield a massive amount of data. Given the increasing complexity and growing interaction across diverse bodies of knowledge it is becoming imperative to define a platform to properly support collaborative research and track origin, accuracy and use of data. This paper starts by defining a set of methods leveraging scientific principles and advocating the importance of those methods in multidisciplinary, computer intensive fields like computational finance. The next part of this paper defines a class of systems called scientific support systems, vis-a-vis usages in other research fields such as bioinformatics, physics and engineering. We outline a basic set of fundamental concepts, and list our goals and motivation for leveraging such systems to enable large-scale investigation, "crowd powered science", in economics. The core of this paper provides an outline of FRACTI in five steps. First we present definitions related to scientific support systems intrinsic to finance and describe common characteristics of financial use cases. The second step concentrates on what can be exchanged through the definition of shareable entities called contributions. The third step is the description of a classification system for building blocks of the conceptual framework, called facets. The fourth step introduces the meta-model that will enable provenance tracking and representation of data fragments and simulation. Finally we describe intended cases of use to highlight main strengths of FRACTI: application of the scientific method for investigation in computational finance, large-scale collaboration and simulation.

q-fin.CP↗

arXiv2020

VLSTM: Very Long Short-Term Memory Networks for High-Frequency Trading

Financial trading is at the forefront of time-series analysis, and has grown hand-in-hand with it. The advent of electronic trading has allowed complex machine learning solutions to enter the field of financial trading. Financial markets have both long term and short term signals and thus a good predictive model in financial trading should be able to incorporate them together. One of the most sought after forms of electronic trading is high-frequency trading (HFT), typically known for microsecond sensitive changes, which results in a tremendous amount of data. LSTMs are one of the most capable variants of the RNN family that can handle long-term dependencies, but even they are not equipped to handle such long sequences of the order of thousands of data points like in HFT. We propose very-long short term memory networks, or VLSTMs, to deal with such extreme length sequences. We explore the importance of VLSTMs in the context of HFT. We compare our model on publicly available dataset and got a 3.14\% increase in F1-score over the existing state-of-the-art time-series forecasting models. We also show that our model has great parallelization potential, which is essential for practical purposes when trading on such markets.

cs.LG↗

arXiv2018

Diversification, Volatility, and Surprising Alpha

It has been widely observed that capitalization-weighted indexes can be beaten by surprisingly simple, systematic investment strategies. Indeed, in the U.S. stock market, equal-weighted portfolios, random-weighted portfolios, and other naive, non- optimized portfolios tend to outperform a capitalization-weighted index over the long term. This outperformance is generally attributed to beneficial factor exposures. Here, we provide a deeper, more general explanation of this phenomenon by decomposing portfolio log-returns into an average growth and an excess growth component. Using a rank-based empirical study we argue that the excess growth component plays the major role in explaining the outperformance of naive portfolios. In particular, individual stock growth rates are not as critical as is traditionally assumed.

q-fin.PM↗

arXiv2018

Mathematics of Market Microstructure under Asymmetric Information

These are the lecture notes for the summer course given for 2018 Mathematical Finance Summer School at Shandong Unversity. It contains a brief introduction to the Kyle model and the related topics in filtering, enlargement of filtrations and Markov bridges.

q-fin.TR↗

arXiv2018

BSE: A Minimal Simulation of a Limit-Order-Book Stock Exchange

This paper describes the design, implementation, and successful use of the Bristol Stock Exchange (BSE), a novel minimal simulation of a centralised financial market, based on a Limit Order Book (LOB) such as is common in major stock exchanges. Construction of BSE was motivated by the fact that most of the world's major financial markets have automated, with trading activity that previously was the responsibility of human traders now being performed by high-speed autonomous automated trading systems. Research aimed at understanding the dynamics of this new style of financial market is hampered by the fact that no operational real-world exchange is ever likely to allow experimental probing of that market while it is open and running live, forcing researchers to work primarily from time-series of past trading data. Similarly, university-level education of the engineers who can create next-generation automated trading systems requires that they have hands-on learning experience in a sufficiently realistic teaching environment. BSE as described here addresses both those needs: it has been successfully used for teaching and research in a leading UK university since 2012, and the BSE program code is freely available as open-source on GitHuB.

cs.CE↗

arXiv2018

Insider Trading with Penalties

We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the demand of the insider and the price functions are in general non-linear and remain analytically tractable because the expected price function is linear. We use this result to investigate the trade off between price efficiency and 'fairness': we consider a regulator that wants to minimise post-trade standard deviation for a given level of uninformed traders' losses. The minimisation is over the function space of penalties; for each possible penalty, our existence and uniqueness theorem allows to define unambiguously the post-trade standard deviation and the uninformed traders' losses that prevail in equilibrium.Optimal penalties are characterized in closed-form. They must increase quickly with the magnitude of the insider's order for small orders and become flat for large orders: in cases where the fundamental realizes at very high or very low values, the insider finds it optimal to trade despite the high penalty. Although such trades-if they occur-are costly for liquidity traders, they signal extreme events and therefore incorporate a lot of information into prices. We generalize this result in two directions by imposing a budget constraint on the regulator and considering the cases of either non-pecuniary or pecuniary penalties. In the first case, we establish that optimal penalties are a subset of the previously optimal penalties: the patterns of equilibrium trade volumes and prices is unchanged. In the second case, we also fully characterize the constrained efficient points and penalties and show that new patterns emerge in the demand schedules of the insider trader and the associated price functions.

q-fin.TR↗

arXiv2021

State-dependent Hawkes processes and their application to limit order book modelling

We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The excitation kernel of the counting process depends on the state process that, reciprocally, switches state when there is an event in the counting process. We first establish the existence and uniqueness of state-dependent Hawkes processes and explain how they can be simulated. Then we develop maximum likelihood estimation methodology for parametric specifications of the process. We apply state-dependent Hawkes processes to high-frequency limit order book data, allowing us to build a novel model that captures the feedback loop between the order flow and the shape of the limit order book. We estimate two specifications of the model, using the bid-ask spread and the queue imbalance as state variables, and find that excitation effects in the order flow are strongly state-dependent. Additionally, we find that the endogeneity of the order flow, measured by the magnitude of excitation, is also state-dependent, being more pronounced in disequilibrium states of the limit order book.

q-fin.ST↗

arXiv2018

A model of adaptive, market behavior generating positive returns, volatility and system risk

We describe a simple model for speculative trading based on adaptive behavior of economic agents.The adaptive behavior is expressed through a feedback mechanism for changing agents' stock-to-bond ratios, depending on the past performance of their portfolios.The stock price is set according to the demand-supply for the asset derived from the agents' target risk levels. Using the methodology of agent-based modeling we show that agents, acting endogenously and adaptively, create a persistent price bubble. The price dynamics generated by the trading process does not reveal any singularities, however the process is accompanied by growing aggregated risk that indicates increasing likelihood of a crash.

q-fin.TR↗

arXiv2022

Closed-form approximations in multi-asset market making

A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functions of many multi-asset extensions of the Avellaneda-Stoikov model. These approximations or proxies can be used (i) as heuristic evaluation functions, (ii) as initial value functions in reinforcement learning algorithms, and/or (iii) directly to design quoting strategies through a greedy approach. Regarding the latter, our results lead to new and easily interpretable closed-form approximations for the optimal quotes, both in the finite-horizon case and in the asymptotic (ergodic) regime.

q-fin.TR↗

arXiv2019

Mid-price estimation for European corporate bonds: a particle filtering approach

In most illiquid markets, there is no obvious proxy for the market price of an asset. The European corporate bond market is an archetypal example of such an illiquid market where mid-prices can only be estimated with a statistical model. In this OTC market, dealers / market makers only have access, indeed, to partial information about the market. In real time, they know the price associated with their trades on the dealer-to-dealer (D2D) and dealer-to-client (D2C) markets, they know the result of the requests for quotes (RFQ) they answered, and they have access to composite prices (e.g., Bloomberg CBBT). This paper presents a Bayesian method for estimating the mid-price of corporate bonds by using the real-time information available to a dealer. This method relies on recent ideas coming from the particle filtering / sequential Monte-Carlo literature.

q-fin.TR↗

arXiv2019

Enhancing Stock Movement Prediction with Adversarial Training

This paper contributes a new machine learning solution for stock movement prediction, which aims to predict whether the price of a stock will be up or down in the near future. The key novelty is that we propose to employ adversarial training to improve the generalization of a neural network prediction model. The rationality of adversarial training here is that the input features to stock prediction are typically based on stock price, which is essentially a stochastic variable and continuously changed with time by nature. As such, normal training with static price-based features (e.g. the close price) can easily overfit the data, being insufficient to obtain reliable models. To address this problem, we propose to add perturbations to simulate the stochasticity of price variable, and train the model to work well under small yet intentional perturbations. Extensive experiments on two real-world stock data show that our method outperforms the state-of-the-art solution with 3.11% relative improvements on average w.r.t. accuracy, validating the usefulness of adversarial training for stock prediction task.

q-fin.TR↗

arXiv2018

Forecasting of Jump Arrivals in Stock Prices: New Attention-based Network Architecture using Limit Order Book Data

The existing literature provides evidence that limit order book data can be used to predict short-term price movements in stock markets. This paper proposes a new neural network architecture for predicting return jump arrivals in equity markets with high-frequency limit order book data. This new architecture, based on Convolutional Long Short-Term Memory with Attention, is introduced to apply time series representation learning with memory and to focus the prediction attention on the most important features to improve performance. The data set consists of order book data on five liquid U.S. stocks. The use of the attention mechanism makes it possible to analyze the importance of the inclusion limit order book data and other input variables. By using this mechanism, we provide evidence that the use of limit order book data was found to improve the performance of the proposed model in jump prediction, either clearly or marginally, depending on the underlying stock. This suggests that path-dependence in limit order book markets is a stock specific feature. Moreover, we find that the proposed approach with an attention mechanism outperforms the multi-layer perceptron network as well as the convolutional neural network and Long Short-Term memory model.

q-fin.TR↗

arXiv2018

Price Discovery and the Accuracy of Consolidated Data Feeds in the U.S. Equity Markets

Both the scientific community and the popular press have paid much attention to the speed of the Securities Information Processor, the data feed consolidating all trades and quotes across the US stock market. Rather than the speed of the Securities Information Processor, or SIP, we focus here on its accuracy. Relying on Trade and Quote data, we provide various measures of SIP latency relative to high-speed data feeds between exchanges, known as direct feeds. We use first differences to highlight not only the divergence between the direct feeds and the SIP, but also the fundamental inaccuracy of the SIP. We find that as many as 60 percent or more of trades are reported out of sequence for stocks with high trade volume, therefore skewing simple measures such as returns. While not yet definitive, this analysis supports our preliminary conclusion that the underlying infrastructure of the SIP is currently unable to keep pace with the trading activity in today's stock market.

q-fin.TR↗

arXiv2018

Deep Learning can Replicate Adaptive Traders in a Limit-Order-Book Financial Market

We report successful results from using deep learning neural networks (DLNNs) to learn, purely by observation, the behavior of profitable traders in an electronic market closely modelled on the limit-order-book (LOB) market mechanisms that are commonly found in the real-world global financial markets for equities (stocks & shares), currencies, bonds, commodities, and derivatives. Successful real human traders, and advanced automated algorithmic trading systems, learn from experience and adapt over time as market conditions change; our DLNN learns to copy this adaptive trading behavior. A novel aspect of our work is that we do not involve the conventional approach of attempting to predict time-series of prices of tradeable securities. Instead, we collect large volumes of training data by observing only the quotes issued by a successful sales-trader in the market, details of the orders that trader is executing, and the data available on the LOB (as would usually be provided by a centralized exchange) over the period that the trader is active. In this paper we demonstrate that suitably configured DLNNs can learn to replicate the trading behavior of a successful adaptive automated trader, an algorithmic system previously demonstrated to outperform human traders. We also demonstrate that DLNNs can learn to perform better (i.e., more profitably) than the trader that provided the training data. We believe that this is the first ever demonstration that DLNNs can successfully replicate a human-like, or super-human, adaptive trader operating in a realistic emulation of a real-world financial market. Our results can be considered as proof-of-concept that a DLNN could, in principle, observe the actions of a human trader in a real financial market and over time learn to trade equally as well as that human trader, and possibly better.

cs.CE↗

arXiv2018

Optimal trading using signals

In this paper we propose a mathematical framework to address the uncertainty emergingwhen the designer of a trading algorithm uses a threshold on a signal as a control. We rely ona theorem by Benveniste and Priouret to deduce our Inventory Asymptotic Behaviour (IAB)Theorem giving the full distribution of the inventory at any point in time for a well formulatedtime continuous version of the trading algorithm.Since this is the first time a paper proposes to address the uncertainty linked to the use of athreshold on a signal for trading, we give some structural elements about the kind of signals thatare using in execution. Then we show how to control this uncertainty for a given cost function.There is no closed form solution to this control, hence we propose several approximation schemesand compare their performances.Moreover, we explain how to apply the IAB Theorem to any trading algorithm drivenby a trading speed. It is not needed to control the uncertainty due to the thresholding of asignal to exploit the IAB Theorem; it can be applied ex-post to any traditional trading algorithm.

q-fin.TR↗

arXiv2018

Endogeneous Dynamics of Intraday Liquidity

In this paper we investigate the endogenous information contained in four liquidity variables at a five minutes time scale on equity markets around the world: the traded volume, the bid-ask spread, the volatility and the volume at first limits of the orderbook. In the spirit of Granger causality, we measure the level of information by the level of accuracy of linear autoregressive models. This empirical study is carried out on a dataset of more than 300 stocks from four different markets (US, UK, Japan and Hong Kong) from a period of over five years. We discuss the obtained performances of autoregressive (AR) models on stationarized versions of the variables, focusing on explaining the observed differences between stocks. Since empirical studies are often conducted at this time scale, we believe it is of paramount importance to document endogenous dynamics in a simple framework with no addition of supplemental information. Our study can hence be used as a benchmark to identify exogenous effects. On the other hand, most optimal trading frameworks (like the celebrated Almgren and Chriss one), focus on computing an optimal trading speed at a frequency close to the one we consider. Such frameworks very often take i.i.d. assumptions on liquidity variables; this paper document the auto-correlations emerging from real data, opening the door to new developments in optimal trading.

q-fin.TR↗

arXiv2018

Risk-Neutral Pricing and Hedging of In-Play Football Bets

A risk-neutral valuation framework is developed for pricing and hedging in-play football bets based on modelling scores by independent Poisson processes with constant intensities. The Fundamental Theorems of Asset Pricing are applied to this set-up which enables us to derive novel arbitrage-free valuation formulæ for contracts currently traded in the market. We also describe how to calibrate the model to the market and how trades can be replicated and hedged.

q-fin.TR↗

arXiv2018

How to Increase Global Wealth Inequality for Fun and Profit

We point out a simple equities trading strategy that allows a sufficiently large, market-neutral, quantitative hedge fund to achieve outsized returns while simultaneously contributing significantly to increasing global wealth inequality. Overnight and intraday return distributions in major equity indices in the United States, Canada, France, Germany, and Japan suggest a few such firms have been implementing this strategy successfully for more than twenty-five years.

econ.GN↗