Quantitative Finance

We develop a fundamentally different stochastic dynamic programming model of trading costs. Built on a strong theoretical foundation, our model provides insights to market participants by splitting the overall move of the security price during the duration of an order into the Market Impact (price move caused by their actions) and Market Timing (price move caused by everyone else) components. We derive formulations of this model under different laws of motion of the security prices, starting with a simple benchmark scenario and extending this to include multiple sources of uncertainty, liquidity constraints due to volume curve shifts and relating trading costs to the spread. We develop a numerical framework that can be used to obtain optimal executions under any law of motion of prices and demonstrate the tremendous practical applicability of our theoretical methodology including the powerful numerical techniques to implement them. Our decomposition of trading costs into Market Impact and Market Timing allows us to deduce the zero sum game nature of trading costs. It holds numerous lessons for dealing with complex systems, wherein reducing the complexity by splitting the many sources of uncertainty can lead to better insights in the decision process.

This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient and specifically designed to take advantage of the spatial structure of limit order books. The new architecture yields a low-dimensional model of price movements deep into the limit order book, allowing more effective use of information from deep in the limit order book (i.e., many levels beyond the best bid and best ask). This "spatial neural network" models the joint distribution of the state of the limit order book at a future time conditional on the current state of the limit order book. The spatial neural network outperforms other models such as the naive empirical model, logistic regression (with nonlinear features), and a standard neural network architecture. Both neural networks strongly outperform the logistic regression model. Due to its more effective use of information deep in the limit order book, the spatial neural network especially outperforms the standard neural network in the tail of the distribution, which is important for risk management applications. The models are trained and tested on nearly 500 stocks. Techniques from deep learning such as dropout are employed to improve performance. Due to the significant computational challenges associated with the large amount of data, models are trained with a cluster of 50 GPUs.

Market by order (MBO) data - a detailed feed of individual trade instructions for a given stock on an exchange - is arguably one of the most granular sources of microstructure information. While limit order books (LOBs) are implicitly derived from it, MBO data is largely neglected by current academic literature which focuses primarily on LOB modelling. In this paper, we demonstrate the utility of MBO data for forecasting high-frequency price movements, providing an orthogonal source of information to LOB snapshots. We provide the first predictive analysis on MBO data by carefully introducing the data structure and presenting a specific normalisation scheme to consider level information in order books and to allow model training with multiple instruments. Through forecasting experiments using deep neural networks, we show that while MBO-driven and LOB-driven models individually provide similar performance, ensembles of the two can lead to improvements in forecasting accuracy -- indicating that MBO data is additive to LOB-based features.

The present work addresses theoretical and practical questions in the domain of Deep Learning for High Frequency Trading. State-of-the-art models such as Random models, Logistic Regressions, LSTMs, LSTMs equipped with an Attention mask, CNN-LSTMs and MLPs are reviewed and compared on the same tasks, feature space and dataset, and then clustered according to pairwise similarity and performance metrics. The underlying dimensions of the modeling techniques are hence investigated to understand whether these are intrinsic to the Limit Order Book's dynamics. We observe that the Multilayer Perceptron performs comparably to or better than state-of-the-art CNN-LSTM architectures indicating that dynamic spatial and temporal dimensions are a good approximation of the LOB's dynamics, but not necessarily the true underlying dimensions.

This paper sets forth a framework for deep reinforcement learning as applied to market making (DRLMM) for cryptocurrencies. Two advanced policy gradient-based algorithms were selected as agents to interact with an environment that represents the observation space through limit order book data, and order flow arrival statistics. Within the experiment, a forward-feed neural network is used as the function approximator and two reward functions are compared. The performance of each combination of agent and reward function is evaluated by daily and average trade returns. Using this DRLMM framework, this paper demonstrates the effectiveness of deep reinforcement learning in solving stochastic inventory control challenges market makers face.

A microscopic model is established for financial Brownian motion from the direct observation of the dynamics of high-frequency traders (HFTs) in a foreign exchange market. Furthermore, a theoretical framework parallel to molecular kinetic theory is developed for the systematic description of the financial market from microscopic dynamics of HFTs. We report first on a microscopic empirical law of traders' trend-following behavior by tracking the trajectories of all individuals, which quantifies the collective motion of HFTs but has not been captured in conventional order-book models. We next introduce the corresponding microscopic model of HFTs and present its theoretical solution paralleling molecular kinetic theory: Boltzmann-like and Langevin-like equations are derived from the microscopic dynamics via the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. Our model is the first microscopic model that has been directly validated through data analysis of the microscopic dynamics, exhibiting quantitative agreements with mesoscopic and macroscopic empirical results.

We propose a design for schedule-based execution trading strategies based on uncertainty bands. This formulation: 1) simplifies strategy specification and implementation; 2) provides for flexible allocation among passive, opportunistic, aggressive, and dark pool crossing execution tactics; 3) allows for rapid enhancements as new optimization methods, scheduling techniques, alpha models, and execution tactics are developed; and 4) yields information at macroscopic (strategic) and microscopic (tactical) levels that is easily published to trading databases and front-end applications.

Based on iterative optimization and activation function in deep learning, we proposed a new analytical framework of high-frequency trading information, that reduced structural loss in the assembly of Volume-synchronized probability of Informed Trading ( VPIN ), Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Support Vector Machine (SVM) to make full use of the order book information. Amongst the return acquisition procedure in market-making transactions, uncovering the relationship between discrete dimensional data from the projection of high-dimensional time-series would significantly improve the model effect. VPIN would prejudge market liquidity, and this effectiveness backtested with CSI300 futures return.

We propose a mathematical procedure for finding informed trader activities in European-style options and their underlying asset. The regression model (9) with moving average component was written. Being added to it ARMA-process for log-price differences of underlying asset, the generalized model is written as Vector ARMA, stable at abs(ro)<1. We also constructed an informed trader activity presence criterion. Using TAIFEX option prices we investigate whether such activity was at the market. We found that there is no significant influence for pricing process made by major market players.

We propose the application of a high-speed maximum likelihood clustering algorithm to detect temporal financial market states, using correlation matrices estimated from intraday market microstructure features. We first determine the ex-ante intraday temporal cluster configurations to identify market states, and then study the identified temporal state features to extract state signature vectors which enable online state detection. The state signature vectors serve as low-dimensional state descriptors which can be used in learning algorithms for optimal planning in the high-frequency trading domain. We present a feasible scheme for real-time intraday state detection from streaming market data feeds. This study identifies an interesting hierarchy of system behaviour which motivates the need for time-scale-specific state space reduction for participating agents.