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arXiv2021

Protecting Pegged Currency Markets from Speculative Investors

We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever increasing risky position in foreign reserves. We describe this situation mathematically by means of two coupled singular control problems, where the common singularity arises from a local time along a random curve. Our first result identifies a certain local time as that central bank strategy for which this risk position is minimized. We then consider the worst-case situation the central bank may face by identifying that strategy of the strategic investor that maximizes the expected inventory of the central bank under a cost criterion, thus establishing a Stackelberg equilibrium in our model.

q-fin.MF↗

arXiv2018

The Power of Trading Polarity: Evidence from China Stock Market Crash

The imbalance of buying and selling functions profoundly in the formation of market trends, however, a fine-granularity investigation of the imbalance is still missing. This paper investigates a unique transaction dataset that enables us to inspect the imbalance of buying and selling on the man-times level at high frequency, what we call 'trading polarity', for a large cross-section of stocks from Shenzhen Stock Exchange. The trading polarity measures the market sentiment toward stocks from a view of very essence of trading desire. When using the polarity to examine market crash, we find that trading polarity successfully reflects the changing of market-level behavior in terms of its flipping times, depth, and length. We further investigate the relationship between polarity and return. At market-level, trading polarity is negatively correlated with returns, while at stock-level, this correlation changes according to market conditions, which becomes a good signal of market psychology transition. Also, the significant correlation disclosed by the market polarity and market emotion implies that our presented polarity, which essentially calculated in the context of high-frequency trading data, can real-timely reflect the sentiment of the market. The trading polarity indeed provides a new way to understand and foresee the market behavior.

q-fin.CP↗

arXiv2018

Dynamical regularities of US equities opening and closing auctions

We first investigate the evolution of opening and closing auctions volumes of US equities along the years. We then report dynamical properties of pre-auction periods: the indicative match price is strongly mean-reverting because the imbalance is; the final auction price reacts to a single auction order placement or cancellation in markedly different ways in the opening and closing auctions when computed conditionally on imbalance improving or worsening events; the indicative price reverts towards the mid price of the regular limit order book but is not especially bound to the spread.

q-fin.TR↗

arXiv2021

Simple Bounds for Utility Maximization with Small Transaction Costs

Using elementary arguments, we show how to derive $\mathbf{L}_p$-error bounds for the approximation of frictionless wealth process in markets with proportional transaction costs. For utilities with bounded risk aversion, these estimates yield lower bounds for the frictional value function, which pave the way for its asymptotic analysis using stability results for viscosity solutions. Using tools from Malliavin calculus, we also derive simple sufficient conditions for the regularity of frictionless optimal trading strategies, the second main ingredient for the asymptotic analysis of small transaction costs.

q-fin.PM↗

arXiv2018

Optimal inventory management and order book modeling

We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [14, 20, 21], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy.

q-fin.TR↗

arXiv2019

Mean Field Games with Partial Information for Algorithmic Trading

Financial markets are often driven by latent factors which traders cannot observe. Here, we address an algorithmic trading problem with collections of heterogeneous agents who aim to perform optimal execution or statistical arbitrage, where all agents filter the latent states of the world, and their trading actions have permanent and temporary price impact. This leads to a large stochastic game with heterogeneous agents. We solve the stochastic game by investigating its mean-field game (MFG) limit, with sub-populations of heterogeneous agents, and, using a convex analysis approach, we show that the solution is characterized by a vector-valued forward-backward stochastic differential equation (FBSDE). We demonstrate that the FBSDE admits a unique solution, obtain it in closed-form, and characterize the optimal behaviour of the agents in the MFG equilibrium. Moreover, we prove the MFG equilibrium provides an $ε$-Nash equilibrium for the finite player game. We conclude by illustrating the behaviour of agents using the optimal MFG strategy through simulated examples.

q-fin.MF↗

arXiv2018

Theoretical and empirical analysis of trading activity

Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades $N$, the traded volume $V$, the asset price $P$, the squared volatility $σ^2$, the bid-ask spread $S$ and the cost of trading $C$. Different reasonings result in simple proportionality relations ("scaling laws") between these variables. A basic proportionality is established between the trading activity and the squared volatility, i.e., $N \sim σ^2$. More sophisticated relations are the so called 3/2-law $N^{3/2} \sim σP V /C$ and the intriguing scaling $N \sim (σP/S)^2$. We prove that these "scaling laws" are the only possible relations for considered sets of variables by means of a well-known argument from physics: dimensional analysis. Moreover, we provide empirical evidence based on data from the NASDAQ stock exchange showing that the sophisticated relations hold with a certain degree of universality. Finally, we discuss the time scaling of the volatility $σ$, which turns out to be more subtle than one might naively expect.

q-fin.TR↗

arXiv2019

A Score-Driven Conditional Correlation Model for Noisy and Asynchronous Data: an Application to High-Frequency Covariance Dynamics

The analysis of the intraday dynamics of correlations among high-frequency returns is challenging due to the presence of asynchronous trading and market microstructure noise. Both effects may lead to significant data reduction and may severely underestimate correlations if traditional methods for low-frequency data are employed. We propose to model intraday log-prices through a multivariate local-level model with score-driven covariance matrices and to treat asynchronicity as a missing value problem. The main advantages of this approach are: (i) all available data are used when filtering correlations, (ii) market microstructure noise is taken into account, (iii) estimation is performed through standard maximum likelihood methods. Our empirical analysis, performed on 1-second NYSE data, shows that opening hours are dominated by idiosyncratic risk and that a market factor progressively emerges in the second part of the day. The method can be used as a nowcasting tool for high-frequency data, allowing to study the real-time response of covariances to macro-news announcements and to build intraday portfolios with very short optimization horizons.

q-fin.TR↗

arXiv2018

Optimal liquidity-based trading tactics

We consider an agent who needs to buy (or sell) a relatively small amount of asset over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity using limit orders, market orders and cancellations. To solve the agent's control problem, we build an order book model and optimize an expected utility function based on our price impact. We derive the equations satisfied by the optimal strategy and solve them numerically. Moreover, we show that our optimal tactic enables us to outperform significantly naive execution strategies.

q-fin.TR↗

arXiv2018

Universal features of price formation in financial markets: perspectives from Deep Learning

Using a large-scale Deep Learning approach applied to a high-frequency database containing billions of electronic market quotes and transactions for US equities, we uncover nonparametric evidence for the existence of a universal and stationary price formation mechanism relating the dynamics of supply and demand for a stock, as revealed through the order book, to subsequent variations in its market price. We assess the model by testing its out-of-sample predictions for the direction of price moves given the history of price and order flow, across a wide range of stocks and time periods. The universal price formation model is shown to exhibit a remarkably stable out-of-sample prediction accuracy across time, for a wide range of stocks from different sectors. Interestingly, these results also hold for stocks which are not part of the training sample, showing that the relations captured by the model are universal and not asset-specific. The universal model --- trained on data from all stocks --- outperforms, in terms of out-of-sample prediction accuracy, asset-specific linear and nonlinear models trained on time series of any given stock, showing that the universal nature of price formation weighs in favour of pooling together financial data from various stocks, rather than designing asset- or sector-specific models as commonly done. Standard data normalizations based on volatility, price level or average spread, or partitioning the training data into sectors or categories such as large/small tick stocks, do not improve training results. On the other hand, inclusion of price and order flow history over many past observations is shown to improve forecasting performance, showing evidence of path-dependence in price dynamics.

q-fin.ST↗

arXiv2018

Pricing Financial Derivatives Subject to Counterparty Risk and Credit Value Adjustment

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the literature, we emphasize that the market value of a defaultable derivative is actually a risky value rather than a risk-free value. Credit value adjustment (CVA) is also elaborated. A practical framework is developed for pricing defaultable derivatives and calculating their CVAs at a portfolio level.

q-fin.PR↗

arXiv2018

Optimal liquidation under stochastic price impact

We assume a continuous-time price impact model similar to Almgren-Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop trading strategies for a trader who desires to liquidate his inventory but faces price impact as a result of his trading. For a fixed trading horizon, we perform coefficient expansion on the Hamilton-Jacobi-Bellman equation associated with the trader's value function. The coefficient expansion yields a sequence of partial differential equations that we solve to give closed-form approximations to the value function and optimal liquidation strategy. We examine some special cases of the optimal liquidation problem and give financial interpretations of the approximate liquidation strategies in these cases. Finally, we provide numerical examples to demonstrate the effectiveness of the approximations.

q-fin.TR↗

arXiv2018

Market Making via Reinforcement Learning

Market making is a fundamental trading problem in which an agent provides liquidity by continually offering to buy and sell a security. The problem is challenging due to inventory risk, the risk of accumulating an unfavourable position and ultimately losing money. In this paper, we develop a high-fidelity simulation of limit order book markets, and use it to design a market making agent using temporal-difference reinforcement learning. We use a linear combination of tile codings as a value function approximator, and design a custom reward function that controls inventory risk. We demonstrate the effectiveness of our approach by showing that our agent outperforms both simple benchmark strategies and a recent online learning approach from the literature.

cs.AI↗

arXiv2018

Co-impact: Crowding effects in institutional trading activity

This paper is devoted to the important yet unexplored subject of crowding effects on market impact, that we call "co-impact". Our analysis is based on a large database of metaorders by institutional investors in the U.S. equity market. We find that the market chiefly reacts to the net order flow of ongoing metaorders, without individually distinguishing them. The joint co-impact of multiple contemporaneous metaorders depends on the total number of metaorders and their mutual sign correlation. Using a simple heuristic model calibrated on data, we reproduce very well the different regimes of the empirical market impact curves as a function of volume fraction $ϕ$: square-root for large $ϕ$, linear for intermediate $ϕ$, and a finite intercept $I_0$ when $ϕ\to 0$. The value of $I_0$ grows with the sign correlation coefficient. Our study sheds light on an apparent paradox: How can a non-linear impact law survive in the presence of a large number of simultaneously executed metaorders?

q-fin.TR↗

arXiv2018

Application of Probabilistic Graphical Models in Forecasting Crude Oil Price

The dissertation investigates the application of Probabilistic Graphical Models (PGMs) in forecasting the price of Crude Oil. This research is important because crude oil plays a very pivotal role in the global economy hence is a very critical macroeconomic indicator of the industrial growth. Given the vast amount of macroeconomic factors affecting the price of crude oil such as supply of oil from OPEC countries, demand of oil from OECD countries, geopolitical and geoeconomic changes among many other variables - probabilistic graphical models (PGMs) allow us to understand by learning the graphical structure. This dissertation proposes condensing data numerous Crude Oil factors into a graphical model in the attempt of creating a accurate forecast of the price of crude oil. The research project experiments with using different libraries in Python in order to construct models of the crude oil market. The experiments in this thesis investigate three main challenges commonly presented while trading oil in the financial markets. The first challenge it investigates is the process of learning the structure of the oil markets; thus allowing crude oil traders to understand the different physical market factors and macroeconomic indicators affecting crude oil markets and how they are \textit{causally} related. The second challenge it solves is the exploration and exploitation of the available data and the learnt structure in predicting the behaviour of the oil markets. The third challenge it investigates is how to validate the performance and reliability of the constructed model in order for it to be deployed in the financial markets. A design and implementation of a probabilistic framework for forecasting the price of crude oil is also presented as part of the research.

q-fin.TR↗

arXiv2018

Quantifying macroeconomic expectations in stock markets using Google Trends

Among other macroeconomic indicators, the monthly release of U.S. unemployment rate figures in the Employment Situation report by the U.S. Bureau of Labour Statistics gets a lot of media attention and strongly affects the stock markets. I investigate whether a profitable investment strategy can be constructed by predicting the likely changes in U.S. unemployment before the official news release using Google query volumes for related search terms. I find that massive new data sources of human interaction with the Internet not only improves U.S. unemployment rate predictability, but can also enhance market timing of trading strategies when considered jointly with macroeconomic data. My results illustrate the potential of combining extensive behavioural data sets with economic data to anticipate investor expectations and stock market moves.

q-fin.TR↗

arXiv2019

Optimal make-take fees for market making regulation

We consider an exchange who wishes to set suitable make-take fees to attract liquidity on its platform. Using a principal-agent approach, we are able to describe in quasi-explicit form the optimal contract to propose to a market maker. This contract depends essentially on the market maker inventory trajectory and on the volatility of the asset. We also provide the optimal quotes that should be displayed by the market maker. The simplicity of our formulas allows us to analyze in details the effects of optimal contracting with an exchange, compared to a situation without contract. We show in particular that it leads to higher quality liquidity and lower trading costs for investors.

q-fin.TR↗

arXiv2018

Effects of a Price limit Change on Market Stability at the Intraday Horizon in the Korean Stock Market

This paper investigates the effects of a price limit change on the volatility of the Korean stock market's (KRX) intraday stock price process. Based on the most recent transaction data from the KRX, which experienced a change in the price limit on June 15, 2015, we examine the change in realized variance after the price limit change to investigate the overall effects of the change on the intraday market volatility. We then analyze the effects in more detail by applying the discrete Fourier transform (DFT) to the data set. We find evidence that the market becomes more volatile in the intraday horizon because of the increase in the amplitudes of the low-frequency components of the price processes after the price limit change. Therefore, liquidity providers are in a worse situation than they were prior to the change.

q-fin.TR↗