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At least 649 records · Page 36Linked to original sources

arXiv2020

Potential in the Schrodinger equation: estimation from empirical data

A recent model for the stock market calculates future price distributions of a stock as a wave function of a quantum particle confined in an infinite potential well. In such a model the question arose as to how to estimate the classical potential needed for solving the Schrodinger equation. In the present article the method used in that work for evaluating the potential is described, in the simplest version to implement, and more sophisticated implementations are suggested later.

q-fin.GN↗

arXiv2020

The interdependency structure in the Mexican stock exchange: A network approach

Our goal in this paper is to study and characterize the interdependency structure of the Mexican Stock Exchange (mainly stocks from BMV) in the period 2000-2019 and provide visualizations which in a one shot provide a big-picture panorama. To this end, we estimate correlation/concentration matrices from different models and then compute metrics from network theory including eigencentralities and network modularity

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arXiv2020

Extending Deep Reinforcement Learning Frameworks in Cryptocurrency Market Making

There has been a recent surge in interest in the application of artificial intelligence to automated trading. Reinforcement learning has been applied to single- and multi-instrument use cases, such as market making or portfolio management. This paper proposes a new approach to framing cryptocurrency market making as a reinforcement learning challenge by introducing an event-based environment wherein an event is defined as a change in price greater or less than a given threshold, as opposed to by tick or time-based events (e.g., every minute, hour, day, etc.). Two policy-based agents are trained to learn a market making trading strategy using eight days of training data and evaluate their performance using 30 days of testing data. Limit order book data recorded from Bitmex exchange is used to validate this approach, which demonstrates improved profit and stability compared to a time-based approach for both agents when using a simple multi-layer perceptron neural network for function approximation and seven different reward functions.

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arXiv2020

Empirical Study of Market Impact Conditional on Order-Flow Imbalance

In this research, we have empirically investigated the key drivers affecting liquidity in equity markets. We illustrated how theoretical models, such as Kyle's model, of agents' interplay in the financial markets, are aligned with the phenomena observed in publicly available trades and quotes data. Specifically, we confirmed that for small signed order-flows, the price impact grows linearly with increase in the order-flow imbalance. We have, further, implemented a machine learning algorithm to forecast market impact given a signed order-flow. Our findings suggest that machine learning models can be used in estimation of financial variables; and predictive accuracy of such learning algorithms can surpass the performance of traditional statistical approaches. Understanding the determinants of price impact is crucial for several reasons. From a theoretical stance, modelling the impact provides a statistical measure of liquidity. Practitioners adopt impact models as a pre-trade tool to estimate expected transaction costs and optimize the execution of their strategies. This further serves as a post-trade valuation benchmark as suboptimal execution can significantly deteriorate a portfolio performance. More broadly, the price impact reflects the balance of liquidity across markets. This is of central importance to regulators as it provides an all-encompassing explanation of the correlation between market design and systemic risk, enabling regulators to design more stable and efficient markets.

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arXiv2021

Order book dynamics with liquidity fluctuations: limit theorems and large deviations

We propose a class of stochastic models for a dynamics of limit order book with different type of liquidities. Within this class of models we study the one where a spread decreases uniformly, belonging to the class of processes known as a population processes with uniform catastrophes. The law of large numbers (LLN), central limit theorem (CLT) and large deviations (LD) are proved for our model with uniform catastrophes. Our results allow us to satisfactorily explain the volatility and local trends in the prices, relevant empirical characteristics that are observed in this type of markets. Furthermore, it shows us how these local trends and volatility are determined by the typical values of the bid-ask spread. In addition, we use our model to show how large deviations occur in the spread and prices, such as those observed in flash crashes.

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arXiv2020

Optimal execution with liquidity risk in a diffusive order book market

We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon $T$. A trader uses both limit and market orders, and a large market order faces an adverse price movement caused by the liquidity risk. First, we study a single period model where the trader places a limit order and/or a market order at the beginning. We show the behavior of optimal amount of market order, $m^*$, and optimal placement of limit order, $y^*$, under different market conditions. Next, we extend it to a multi-period model, where the trader makes sequential decisions of limit and market orders at multiple time points.

q-fin.CP↗

arXiv2020

Inside the Mind of Investors During the COVID-19 Pandemic: Evidence from the StockTwits Data

We study the investor beliefs, sentiment and disagreement, about stock market returns during the COVID-19 pandemic using a large number of messages of investors on a social media investing platform, \textit{StockTwits}. The rich and multimodal features of StockTwits data allow us to explore the evolution of sentiment and disagreement within and across investors, sectors, and even industries. We find that the sentiment (disagreement) has a sharp decrease (increase) across all investors with any investment philosophy, horizon, and experience between February 19, 2020, and March 23, 2020, where a historical market high followed by a record drop. Surprisingly, these measures have a sharp reverse toward the end of March. However, the performance of these measures across various sectors is heterogeneous. Financial and healthcare sectors are the most pessimistic and optimistic divisions, respectively.

q-fin.ST↗

arXiv2021

From orders to prices: A stochastic description of the limit order book to forecast intraday returns

We propose a microscopic model to describe the dynamics of the fundamental events in the limit order book (LOB): order arrivals and cancellations. It is based on an operator algebra for individual orders and describes their effect on the LOB. The model inputs are arrival and cancellation rate distributions that emerge from individual behavior of traders, and we show how prices and liquidity arise from the LOB dynamics. In a simulation study we illustrate how the model works and highlight its sensitivity with respect to assumptions regarding the collective behavior of market participants. Empirically, we test the model on a LOB snapshot of XETRA, estimate several linearized model specifications, and conduct in- and out-of-sample forecasts.The in-sample results based on contemporaneous information suggest that our model describes returns very well, resulting in an adjusted $R^2$ of roughly 80%. In the more realistic setting where only past information enters the model, we observe an adjusted $R^2$ around 15%. The direction of the next return can be predicted (out-of-sample) with an accuracy above 75% for time horizons below 10 minutes. On average, we obtain an RMSPE that is 10 times lower than values documented in the literature.

q-fin.TR↗

arXiv2020

Trading Foreign Exchange Triplets

We develop the optimal trading strategy for a foreign exchange (FX) broker who must liquidate a large position in an illiquid currency pair. To maximize revenues, the broker considers trading in a currency triplet which consists of the illiquid pair and two other liquid currency pairs. The liquid pairs in the triplet are chosen so that one of the pairs is redundant. The broker is risk-neutral and accounts for model ambiguity in the FX rates to make her strategy robust to model misspecification. When the broker is ambiguity neutral (averse) the trading strategy in each pair is independent (dependent) of the inventory in the other two pairs in the triplet. We employ simulations to illustrate how the robust strategies perform. For a range of ambiguity aversion parameters, we find the mean Profit and Loss (P&L) of the strategy increases and the standard deviation of the P&L decreases as ambiguity aversion increases.

q-fin.TR↗

arXiv2020

A Stochastic LQR Model for Child Order Placement in Algorithmic Trading

Modern Algorithmic Trading ("Algo") allows institutional investors and traders to liquidate or establish big security positions in a fully automated or low-touch manner. Most existing academic or industrial Algos focus on how to "slice" a big parent order into smaller child orders over a given time horizon. Few models rigorously tackle the actual placement of these child orders. Instead, placement is mostly done with a combination of empirical signals and heuristic decision processes. A self-contained, realistic, and fully functional Child Order Placement (COP) model may never exist due to all the inherent complexities, e.g., fragmentation due to multiple venues, dynamics of limit order books, lit vs. dark liquidity, different trading sessions and rules. In this paper, we propose a reductionism COP model that focuses exclusively on the interplay between placing passive limit orders and sniping using aggressive takeout orders. The dynamic programming model assumes the form of a stochastic linear-quadratic regulator (LQR) and allows closed-form solutions under the backward Bellman equations. Explored in detail are model assumptions and general settings, the choice of state and control variables and the cost functions, and the derivation of the closed-form solutions.

q-fin.TR↗

arXiv2020

Non-parametric Estimation of Quadratic Hawkes Processes for Order Book Events

We propose an actionable calibration procedure for general Quadratic Hawkes models of order book events (market orders, limit orders, cancellations). One of the main features of such models is to encode not only the influence of past events on future events but also, crucially, the influence of past price changes on such events. We show that the empirically calibrated quadratic kernel is well described by a diagonal contribution (that captures past realised volatility), plus a rank-one "Zumbach" contribution (that captures the effect of past trends). We find that the Zumbach kernel is a power-law of time, as are all other feedback kernels. As in many previous studies, the rate of truly exogenous events is found to be a small fraction of the total event rate. These two features suggest that the system is close to a critical point -- in the sense that stronger feedback kernels would lead to instabilities.

q-fin.TR↗

arXiv2020

Temporal mixture ensemble models for intraday volume forecasting in cryptocurrency exchange markets

We study the problem of the intraday short-term volume forecasting in cryptocurrency exchange markets. The predictions are built by using transaction and order book data from different markets where the exchange takes place. Methodologically, we propose a temporal mixture ensemble, capable of adaptively exploiting, for the forecasting, different sources of data and providing a volume point estimate, as well as its uncertainty. We provide evidence of the outperformance of our model by comparing its outcomes with those obtained with different time series and machine learning methods. Finally, we discuss the predictions conditional to volume and we find that also in this case machine learning methods outperform econometric models.

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arXiv2020

Recipes for hedging exotics with illiquid vanillas

In this paper, we address the question of the optimal Delta and Vega hedging of a book of exotic options when there are execution costs associated with the trading of vanilla options. In a framework where exotic options are priced using a market model (e.g. a local volatility model recalibrated continuously to vanilla option prices) and vanilla options prices are driven by a stochastic volatility model, we show that, using simple approximations, the optimal dynamic Delta and Vega hedging strategies can be computed easily using variational techniques.

q-fin.TR↗

arXiv2020

Dynamic Coupling and Market Instability

We examine dynamic coupling and feedback effects between High Frequency Traders (HFTs) and how they can destabilize markets. We develop a general framework for modelling dynamic interaction based on recurrence relations, and use this to show how unexpected latency and feedback can trigger oscillatory instability between HFT market makers with inventory constraints. Our analysis suggests that the modelled instability is an unintentional emergent behaviour of the market that does not depend on the complexity of HFT strategies - even apparently stable strategies are vulnerable. Feedback instability can lead to substantial movements in market prices such as price spikes and crashes.

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arXiv2020

On bid and ask side-specific tick sizes

The tick size, which is the smallest increment between two consecutive prices for a given asset, is a key parameter of market microstructure. In particular, the behavior of high frequency market makers is highly related to its value. We take the point of view of an exchange and investigate the relevance of having different tick sizes on the bid and ask sides of the order book. Using an approach based on the model with uncertainty zones, we show that when side-specific tick sizes are suitably chosen, it enables the exchange to improve the quality of liquidity provision.

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arXiv2020

Shallow Neural Hawkes: Non-parametric kernel estimation for Hawkes processes

Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes two major contributions, we first find an unbiased estimator for the log-likelihood estimator of the Hawkes process to enable efficient use of the stochastic gradient descent method for maximum likelihood estimation. The second contribution is, we propose a specific single hidden layered neural network for the non-parametric estimation of the underlying kernels of the MHP. We evaluate the proposed model on both synthetic and real datasets, and find the method has comparable or better performance than existing estimation methods. The use of shallow neural network ensures that we do not compromise on the interpretability of the Hawkes model, while at the same time have the flexibility to estimate any non-standard Hawkes excitation kernel.

stat.ML↗

arXiv2020

An overall view of key problems in algorithmic trading and recent progress

We summarize the fundamental issues at stake in algorithmic trading, and the progress made in this field over the last twenty years. We first present the key problems of algorithmic trading, describing the concepts of optimal execution, optimal placement, and price impact. We then discuss the most recent advances in algorithmic trading through the use of Machine Learning, discussing the use of Deep Learning, Reinforcement Learning, and Generative Adversarial Networks.

q-fin.TR↗

arXiv2021

Optimal trade execution in an order book model with stochastic liquidity parameters

We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both directions and at discrete points in time. We derive an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs. We also discuss several qualitative aspects of optimal strategies, such as existence of profitable round trips or closing the position in one go, and compare our findings with the literature.

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