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arXiv2020

Ascertaining price formation in cryptocurrency markets with DeepLearning

The cryptocurrency market is amongst the fastest-growing of all the financial markets in the world. Unlike traditional markets, such as equities, foreign exchange and commodities, cryptocurrency market is considered to have larger volatility and illiquidity. This paper is inspired by the recent success of using deep learning for stock market prediction. In this work, we analyze and present the characteristics of the cryptocurrency market in a high-frequency setting. In particular, we applied a deep learning approach to predict the direction of the mid-price changes on the upcoming tick. We monitored live tick-level data from $8$ cryptocurrency pairs and applied both statistical and machine learning techniques to provide a live prediction. We reveal that promising results are possible for cryptocurrencies, and in particular, we achieve a consistent $78\%$ accuracy on the prediction of the mid-price movement on live exchange rate of Bitcoins vs US dollars.

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arXiv2020

Robust Market Making via Adversarial Reinforcement Learning

We show that adversarial reinforcement learning (ARL) can be used to produce market marking agents that are robust to adversarial and adaptively-chosen market conditions. To apply ARL, we turn the well-studied single-agent model of Avellaneda and Stoikov [2008] into a discrete-time zero-sum game between a market maker and adversary. The adversary acts as a proxy for other market participants that would like to profit at the market maker's expense. We empirically compare two conventional single-agent RL agents with ARL, and show that our ARL approach leads to: 1) the emergence of risk-averse behaviour without constraints or domain-specific penalties; 2) significant improvements in performance across a set of standard metrics, evaluated with or without an adversary in the test environment, and; 3) improved robustness to model uncertainty. We empirically demonstrate that our ARL method consistently converges, and we prove for several special cases that the profiles that we converge to correspond to Nash equilibria in a simplified single-stage game.

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arXiv2021

A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition

In this work, we study an equilibrium-based continuous asset pricing problem which seeks to form a price process endogenously by requiring it to balance the flow of sales-and-purchase orders in the exchange market, where a large number of agents are interacting through the market price. Adopting a mean field game (MFG) approach, we find a special form of forward-backward stochastic differential equations of McKean-Vlasov type with common noise whose solution provides a good approximate of the market price. We show the convergence of the net order flow to zero in the large N-limit and get the order of convergence in N under some conditions. We also extend the model to a setup with multiple populations where the agents within each population share the same cost and coefficient functions but they can be different population by population.

q-fin.MF↗

arXiv2020

How much is your Strangle worth? On the relative value of the $δ-$Symmetric Strangle under the Black-Scholes model

Trading option strangles is a highly popular strategy often used by market participants to mitigate volatility risks in their portfolios. In this paper we propose a measure of the relative value of a delta-Symmetric Strangle and compute it under the standard Black-Scholes option pricing model. This new measure accounts for the price of the strangle, relative to the Present Value of the spread between the two strikes, all expressed, after a natural re-parameterization, in terms of delta and a volatility parameter. We show that under the standard BS option pricing model, this measure of relative value is bounded by a simple function of delta only and is independent of the time to expiry, the price of the underlying security or the prevailing volatility used in the pricing model. We demonstrate how this bound can be used as a quick {\it benchmark} to assess, regardless the market volatility, the duration of the contract or the price of the underlying security, the market (relative) value of the $δ-$strangle in comparison to its BS (relative) price. In fact, the explicit and simple expression for this measure and bound allows us to also study in detail the strangle's exit strategy and the corresponding {\it optimal} choice for a value of delta.

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arXiv2020

Informed trading, limit order book and implementation shortfall: equilibrium and asymptotics

We propose a static equilibrium model for limit order book where profit-maximizing investors receive an information signal regarding the liquidation value of the asset and execute via a competitive dealer with random initial inventory, who trades against a competitive limit order book populated by liquidity suppliers. We show that an equilibrium exists for bounded signal distributions, obtain closed form solutions for Bernoulli-type signals and propose a straightforward iterative algorithm to compute the equilibrium order book for the general case. We obtain the exact analytic asymptotics for the market impact of large trades and show that the functional form depends on the tail distribution of the private signal of the insiders. In particular, the impact follows a power law if the signal has fat tails while the law is logarithmic in case of lighter tails. Moreover, the tail distribution of the trade volume in equilibrium obeys a power law in our model. We find that the liquidity suppliers charge a minimum bid-ask spread that is independent of the amount of `noise' trading but increasing in the degree of informational advantage of insiders in equilibrium. The model also predicts that the order book flattens as the amount of noise trading increases converging to a model with proportional transactions costs.. Competition among the insiders leads to aggressive trading causing the aggregate profit to vanish in the limiting case $N\to\infty$. The numerical results also show that the spread increases with the number of insiders keeping the other parameters fixed. Finally, an equilibrium may not exist if the liquidation value is unbounded. We conjecture that existence of equilibrium requires a sufficient amount of competition among insiders if the signal distribution exhibit fat tails.

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arXiv2021

A Mean-Field Game Approach to Equilibrium Pricing in Solar Renewable Energy Certificate Markets

Solar Renewable Energy Certificate (SREC) markets are a market-based system that incentivizes solar energy generation. A regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a tradeable certificate for each MWh generated. Firms seek to navigate the market optimally by modulating their SREC generation and trading rates. As such, the SREC market can be viewed as a stochastic game, where agents interact through the SREC price. We study this stochastic game by solving the mean-field game (MFG) limit with sub-populations of heterogeneous agents. Market participants optimize costs accounting for trading frictions, cost of generation, non-linear non-compliance costs, and generation uncertainty. Moreover, we endogenize SREC price through market clearing. We characterize firms' optimal controls as the solution of McKean-Vlasov (MV) FBSDEs and determine the equilibrium SREC price. We establish the existence and uniqueness of a solution to this MV-FBSDE, and prove that the MFG strategies form an $ε$-Nash equilibrium for the finite player game. Finally, we develop a numerical scheme for solving the MV-FBSDEs and conduct a simulation study.

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arXiv2020

Optimal market making with persistent order flow

\noindent We address the issue of market making on electronic markets when taking into account the clustering and long memory properties of market order flows. We consider a market model with one market maker and order flows driven by general Hawkes processes. We formulate the market maker's objective as a stochastic control problem. We characterize an optimal control by proving existence and uniqueness of a viscosity solution to the associated Hamilton-Jacobi-Bellman equation. Finally we propose a fully consistent numerical method allowing to implement this optimal strategy in practice.

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arXiv2020

Disturbing the Peace: Anatomy of the Hostile Takeover of China Vanke Co

Wang Shi, a business mogul who created his empire of wealth from scratch, relished in his fame and basked in the glory of his affluent business. Nothing lasts forever! After mastering the turbulent business of real estate development in his country and therefore enjoying a rising and robust stock price, China Vanke Co. Ltd ("Vanke") founder and Chairman of the Board of Directors, Wang Shi was suddenly presented with a scathing notice from the Hong Kong Stock Exchange: rival Baoneng Group ("Baoneng") filed the regulatory documentation indicating that it had nicodemously acquired 5% of his company and was looking to buy more. Vanke case became brutal and sparked national controversy over corporate governance and the role of Chinese government in capital markets.

q-fin.GN↗

arXiv2020

Effects of MiFID II on stock price formation

This paper examines effects of MiFID II on European stock markets. We study the effects of the new tick size regime, both intraday and in the closing auction. An increase (decrease) in tick size is associated with a decrease (increase) in intraday liquidity, but a more (less) stable market. In the closing auction an increase in tick size has a positive effect on liquidity. Moreover, we report a positive relationship between tick size and transacted volume, in particular in the closing auction. Finally, closing auction volumes increased heavily since MiFID II and price formation in closing auctions became more efficient.

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arXiv2020

A closed-form solution for optimal mean-reverting trading strategies

When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein-Uhlenbeck (O-U) process. Market makers provide liquidity in an attempt to monetize this oscillation. They enter a long position when a security is priced below its estimated equilibrium level, and they enter a short position when a security is priced above its estimated equilibrium level. They hold that position until one of three outcomes occur: (1) they achieve the targeted profit; (2) they experience a maximum tolerated loss; (3) the position is held beyond a maximum tolerated horizon. All market makers are confronted with the problem of defining profit-taking and stop-out levels. More generally, all execution traders acting on behalf of a client must determine at what levels an order must be fulfilled. Those optimal levels can be determined by maximizing the trader's Sharpe ratio in the context of O-U processes via Monte Carlo experiments. This paper develops an analytical framework and derives those optimal levels by using the method of heat potentials.

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arXiv2022

Cryptocurrency Trading: A Comprehensive Survey

In recent years, the tendency of the number of financial institutions including cryptocurrencies in their portfolios has accelerated. Cryptocurrencies are the first pure digital assets to be included by asset managers. Although they have some commonalities with more traditional assets, they have their own separate nature and their behaviour as an asset is still in the process of being understood. It is therefore important to summarise existing research papers and results on cryptocurrency trading, including available trading platforms, trading signals, trading strategy research and risk management. This paper provides a comprehensive survey of cryptocurrency trading research, by covering 146 research papers on various aspects of cryptocurrency trading (e.g., cryptocurrency trading systems, bubble and extreme conditions, prediction of volatility and return, crypto-assets portfolio construction and crypto-assets, technical trading and others). This paper also analyses datasets, research trends and distribution among research objects(contents/properties) and technologies, concluding with some promising opportunities that remain open in cryptocurrency trading.

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arXiv2020

Deep Probabilistic Modelling of Price Movements for High-Frequency Trading

In this paper we propose a deep recurrent architecture for the probabilistic modelling of high-frequency market prices, important for the risk management of automated trading systems. Our proposed architecture incorporates probabilistic mixture models into deep recurrent neural networks. The resulting deep mixture models simultaneously address several practical challenges important in the development of automated high-frequency trading strategies that were previously neglected in the literature: 1) probabilistic forecasting of the price movements; 2) single objective prediction of both the direction and size of the price movements. We train our models on high-frequency Bitcoin market data and evaluate them against benchmark models obtained from the literature. We show that our model outperforms the benchmark models in both a metric-based test and in a simulated trading scenario

q-fin.ST↗

arXiv2020

Deep Recurrent Modelling of Stationary Bitcoin Price Formation Using the Order Flow

In this paper we propose a deep recurrent model based on the order flow for the stationary modelling of the high-frequency directional prices movements. The order flow is the microsecond stream of orders arriving at the exchange, driving the formation of prices seen on the price chart of a stock or currency. To test the stationarity of our proposed model we train our model on data before the 2017 Bitcoin bubble period and test our model during and after the bubble. We show that without any retraining, the proposed model is temporally stable even as Bitcoin trading shifts into an extremely volatile "bubble trouble" period. The significance of the result is shown by benchmarking against existing state-of-the-art models in the literature for modelling price formation using deep learning.

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arXiv2022

How to build a cross-impact model from first principles: Theoretical requirements and empirical results

Trading a financial instrument pushes its price and those of other assets, a phenomenon known as cross-impact. To be of use, cross-impact models must fit data and be well-behaved so they can be applied in applications such as optimal trading. To address these issues, we introduce a set of desirable properties which constrain cross-impact models. We classify cross-impact models according to which properties they satisfy and stress them on three different asset classes to evaluate goodness-of-fit. We find that two models are robust across markets, but only one satisfies all desirable properties and is appropriate for applications.

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arXiv2020

QuantNet: Transferring Learning Across Systematic Trading Strategies

Systematic financial trading strategies account for over 80% of trade volume in equities and a large chunk of the foreign exchange market. In spite of the availability of data from multiple markets, current approaches in trading rely mainly on learning trading strategies per individual market. In this paper, we take a step towards developing fully end-to-end global trading strategies that leverage systematic trends to produce superior market-specific trading strategies. We introduce QuantNet: an architecture that learns market-agnostic trends and use these to learn superior market-specific trading strategies. Each market-specific model is composed of an encoder-decoder pair. The encoder transforms market-specific data into an abstract latent representation that is processed by a global model shared by all markets, while the decoder learns a market-specific trading strategy based on both local and global information from the market-specific encoder and the global model. QuantNet uses recent advances in transfer and meta-learning, where market-specific parameters are free to specialize on the problem at hand, whilst market-agnostic parameters are driven to capture signals from all markets. By integrating over idiosyncratic market data we can learn general transferable dynamics, avoiding the problem of overfitting to produce strategies with superior returns. We evaluate QuantNet on historical data across 3103 assets in 58 global equity markets. Against the top performing baseline, QuantNet yielded 51% higher Sharpe and 69% Calmar ratios. In addition we show the benefits of our approach over the non-transfer learning variant, with improvements of 15% and 41% in Sharpe and Calmar ratios. Code available in appendix.

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arXiv2021

Instabilities in Multi-Asset and Multi-Agent Market Impact Games

We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied & Zhang (2019) and Luo & Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied & Zhang (2019) and Luo & Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M ) of markets.

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arXiv2020

A Deep Reinforcement Learning Framework for Continuous Intraday Market Bidding

The large integration of variable energy resources is expected to shift a large part of the energy exchanges closer to real-time, where more accurate forecasts are available. In this context, the short-term electricity markets and in particular the intraday market are considered a suitable trading floor for these exchanges to occur. A key component for the successful renewable energy sources integration is the usage of energy storage. In this paper, we propose a novel modelling framework for the strategic participation of energy storage in the European continuous intraday market where exchanges occur through a centralized order book. The goal of the storage device operator is the maximization of the profits received over the entire trading horizon, while taking into account the operational constraints of the unit. The sequential decision-making problem of trading in the intraday market is modelled as a Markov Decision Process. An asynchronous distributed version of the fitted Q iteration algorithm is chosen for solving this problem due to its sample efficiency. The large and variable number of the existing orders in the order book motivates the use of high-level actions and an alternative state representation. Historical data are used for the generation of a large number of artificial trajectories in order to address exploration issues during the learning process. The resulting policy is back-tested and compared against a benchmark strategy that is the current industrial standard. Results indicate that the agent converges to a policy that achieves in average higher total revenues than the benchmark strategy.

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arXiv2020

Dual State-Space Model of Market Liquidity: The Chinese Experience 2009-2010

This paper proposes and motivates a dynamical model of the Chinese stock market based on a linear regression in a dual state space connected to the original state space of correlations between the volume-at-price buckets by a Fourier transform. We apply our model to the price migration of executed orders by the Chinese brokerages in 2009-2010. Regulatory brokerage tapes were used to conduct a natural experiment assuming that tapes correspond to randomly assigned, informed and uninformed traders. Our analysis demonstrated that customers' orders were tightly correlated--in a highly nonlinear sense of the neural networks--with the Chinese market sentiment index, significantly correlated with the stock returns and exhibited no correlation with the bellwether bond of the Bank of China. We did not notice any spike of illiquidity transmitting from the US Flash Crash in May 2010 to trading in China.

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