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arXiv2019

Formal verification of trading in financial markets

We introduce a formal framework for analyzing trades in financial markets. An exchange is where multiple buyers and sellers participate to trade. These days, all big exchanges use computer algorithms that implement double sided auctions to match buy and sell requests and these algorithms must abide by certain regulatory guidelines. For example, market regulators enforce that a matching produced by exchanges should be \emph{fair}, \emph{uniform} and \emph{individual rational}. To verify these properties of trades, we first formally define these notions in a theorem prover and then give formal proofs of relevant results on matchings. Finally, we use this framework to verify properties of two important classes of double sided auctions. All the definitions and results presented in this paper are completely formalised in the Coq proof assistant without adding any additional axioms to it.

cs.LO↗

arXiv2019

Stochastic Spread Pairs Trading in the Indian Commodity Market

In this study, we applied a stochastic spread pairs trading strategy on the Indian commodity market. The complete set of commodities were taken whose spot price was available for the period of January 1st 2010 to December 31st 2018 including energy, metals and the agricultural commodity sector. Spot data was taken from the MCX pooled spot prices for 17 commodities. The data was split into training period (January 1st 2010 to 14th March 2017) and testing period(15th Match 2017 to 31st December 2018). The splitting was done using a 80:20 split.Johanssen Cointegration tests were done on training data for pairs of commodities to check for long-run relationship and the cointegrated commodities were selected for formation of the trading process. We found a total of 12 cointegrated pairs out of 136 possible pairs. Cointegration was assumed for the testing period. A single-factor stochastic trading approach was applied on the logarithmic spread of the cointegrated pairs for both the training and testing period.The parameters of stochastic spread model were estimated using differential evolution algorithm. Also parameters for the trading rule were optimized by backtesting on the training period and assumed for the testing period. The results show a sharpe ratio of above 1.4 for all the commodity cointegrated pairs in the backtesing period.

q-fin.TR↗

arXiv2019

Generalized statistical arbitrage concepts and related gain strategies

Generalized statistical arbitrage concepts are introduced corresponding to trading strategies which yield positive gains on average in a class of scenarios rather than almost surely. The relevant scenarios or market states are specified via an information system given by a $σ$-algebra and so this notion contains classical arbitrage as a special case. It also covers the notion of statistical arbitrage introduced in Bondarenko (2003). Relaxing these notions further we introduce generalized profitable strategies which include also static or semi-static strategies. Under standard no-arbitrage there may exist generalized gain strategies yielding positive gains on average under the specified scenarios. In the first part of the paper we characterize these generalized statistical no-arbitrage notions. In the second part of the paper we construct several profitable generalized strategies with respect to various choices of the information system. In particular, we consider several forms of embedded binomial strategies and follow-the-trend strategies as well as partition-type strategies. We study and compare their behaviour on simulated data. Additionally, we find good performance on market data of these simple strategies which makes them profitable candidates for real applications.

q-fin.MF↗

arXiv2019

The Effect of Visual Design in Image Classification

Financial companies continuously analyze the state of the markets to rethink and adjust their investment strategies. While the analysis is done on the digital form of data, decisions are often made based on graphical representations in white papers or presentation slides. In this study, we examine whether binary decisions are better to be decided based on the numeric or the visual representation of the same data. Using two data sets, a matrix of numerical data with spatial dependencies and financial data describing the state of the S&P index, we compare the results of supervised classification based on the original numerical representation and the visual transformation of the same data. We show that, for these data sets, the visual transformation results in higher predictability skill compared to the original form of the data. We suggest thinking of the visual representation of numeric data, effectively, as a combination of dimensional reduction and feature engineering techniques. In particular, if the visual layout encapsulates the full complexity of the data. In this view, thoughtful visual design can guard against overfitting, or introduce new features -- all of which benefit the learning process, and effectively lead to better recognition of meaningful patterns.

cs.CV↗

arXiv2019

Accelerated Share Repurchase and other buyback programs: what neural networks can bring

When firms want to buy back their own shares, they have a choice between several alternatives. If they often carry out open market repurchase, they also increasingly rely on banks through complex buyback contracts involving option components, e.g. accelerated share repurchase contracts, VWAP-minus profit-sharing contracts, etc. The entanglement between the execution problem and the option hedging problem makes the management of these contracts a difficult task that should not boil down to simple Greek-based risk hedging, contrary to what happens with classical books of options. In this paper, we propose a machine learning method to optimally manage several types of buyback contract. In particular, we recover strategies similar to those obtained in the literature with partial differential equation and recombinant tree methods and show that our new method, which does not suffer from the curse of dimensionality, enables to address types of contract that could not be addressed with grid or tree methods.

q-fin.CP↗

arXiv2020

Trading via Image Classification

The art of systematic financial trading evolved with an array of approaches, ranging from simple strategies to complex algorithms all relying, primary, on aspects of time-series analysis. Recently, after visiting the trading floor of a leading financial institution, we noticed that traders always execute their trade orders while observing images of financial time-series on their screens. In this work, we built upon the success in image recognition and examine the value in transforming the traditional time-series analysis to that of image classification. We create a large sample of financial time-series images encoded as candlestick (Box and Whisker) charts and label the samples following three algebraically-defined binary trade strategies. Using the images, we train over a dozen machine-learning classification models and find that the algorithms are very efficient in recovering the complicated, multiscale label-generating rules when the data is represented visually. We suggest that the transformation of continuous numeric time-series classification problem to a vision problem is useful for recovering signals typical of technical analysis.

cs.CV↗

arXiv2019

Liquid Speed: On-Demand Fast Trading at Distributed Exchanges

Exchanges acquire excess processing capacity to accommodate trading activity surges associated with zero-sum high-frequency trader (HFT) "duels." The idle capacity's opportunity cost is an externality of low-latency trading. We build a model of decentralized exchanges (DEX) with flexible capacity. On DEX, HFTs acquire speed in real-time from peer-to-peer networks. The price of speed surges during activity bursts, as HFTs simultaneously race to market. Relative to centralized exchanges, HFTs acquire more speed on DEX, but for shorter timespans. Low-latency "sprints" speed up price discovery without harming liquidity. Overall, speed rents decrease and fewer resources are locked-in to support zero-sum HFT trades.

q-fin.TR↗

arXiv2021

Optimal make take fees in a multi market maker environment

Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimise their quotes in a Nash equilibrium fashion, providing best response to the contract proposed by the principal (the exchange). This contract aims at attracting liquidity on the platform. This is because the wealth of the exchange depends on the arrival of market orders, which is driven by the spread of market makers. We compute the optimal contract in quasi explicit form and also derive the optimal spread policies for the market makers. Several new phenomena appears in this multi market maker setting. In particular we show that it is not necessarily optimal to have a large number of market makers in the presence of a contracting scheme.

q-fin.TR↗

arXiv2019

Taxable Stock Trading with Deep Reinforcement Learning

In this paper, we propose stock trading based on the average tax basis. Recall that when selling stocks, capital gain should be taxed while capital loss can earn certain tax rebate. We learn the optimal trading strategies with and without considering taxes by reinforcement learning. The result shows that tax ignorance could induce more than 62% loss on the average portfolio returns, implying that taxes should be embedded in the environment of continuous stock trading on AI platforms.

q-fin.TR↗

arXiv2020

Hedging Non-Tradable Risks with Transaction Costs and Price Impact

A risk-averse agent hedges her exposure to a non-tradable risk factor $U$ using a correlated traded asset $S$ and accounts for the impact of her trades on both factors. The effect of the agent's trades on $U$ is referred to as cross-impact. By solving the agent's stochastic control problem, we obtain a closed-form expression for the optimal strategy when the agent holds a linear position in $U$. When the exposure to the non-tradable risk factor $ψ(U_T)$ is non-linear, we provide an approximation to the optimal strategy in closed-form, and prove that the value function is correctly approximated by this strategy when cross-impact and risk-aversion are small. We further prove that when $ψ(U_T)$ is non-linear, the approximate optimal strategy can be written in terms of the optimal strategy for a linear exposure with the size of the position changing dynamically according to the exposure's "Delta" under a particular probability measure.

q-fin.MF↗

arXiv2019

An instantaneous market volatility estimation

Working on different aspects of algorithmic trading we empirically discovered a new market invariant. It links together the volatility of the instrument with its traded volume, the average spread and the volume in the order book. The invariant has been tested on different markets and different asset classes. In all cases we did not find significant violation of the invariant. The formula for the invariant was used for the volatility estimation, which we called the instantaneous volatility. Quantitative comparison showed that it reproduces realised volatility better than one-day-ahead GARCH(1,1) prediction. Because of the short-term prediction nature, the instantaneous volatility could be used by algo developers, volatility traders and other market professionals.

q-fin.TR↗

arXiv2019

Latency and Liquidity Risk

Latency (i.e., time delay) in electronic markets affects the efficacy of liquidity taking strategies. During the time liquidity takers process information and send marketable limit orders (MLOs) to the exchange, the limit order book (LOB) might undergo updates, so there is no guarantee that MLOs are filled. We develop a latency-optimal trading strategy that improves the marksmanship of liquidity takers. The interaction between the LOB and MLOs is modelled as a marked point process. Each MLO specifies a price limit so the order can receive worse prices and quantities than those the liquidity taker targets if the updates in the LOB are against the interest of the trader. In our model, the liquidity taker balances the tradeoff between missing trades and the costs of walking the book. We employ techniques of variational analysis to obtain the optimal price limit of each MLO the agent sends. The price limit of a MLO is characterized as the solution to a new class of forward-backward stochastic differential equations (FBSDEs) driven by random measures. We prove the existence and uniqueness of the solution to the FBSDE and numerically solve it to illustrate the performance of the latency-optimal strategies.

q-fin.TR↗

arXiv2019

Random walk model from the point of view of algorithmic trading

Despite the fact that an intraday market price distribution is not normal, the random walk model of price behaviour is as important for the understanding of basic principles of the market as the pendulum model is a starting point of many fundamental theories in physics. This model is a good zero order approximation for liquid fast moving markets where the queue position is less important than the price action. In this paper we present an exact solution for the cost of the static passive slice execution. It is shown, that if a price has a random walk behaviour, there is no optimal limit level for an order execution: all levels have the same execution cost as an immediate aggressive execution at the beginning of the slice. Additionally the estimations for the risk of a limit order as well as the probability of a limit order execution as functions of the slice time and standard deviation of the price are derived.

q-fin.TR↗

arXiv2019

A Review of Changepoint Detection Models

The objective of the change-point detection is to discover the abrupt property changes lying behind the time-series data. In this paper, we firstly summarize the definition and in-depth implication of the changepoint detection. The next stage is to elaborate traditional and some alternative model-based changepoint detection algorithms. Finally, we try to go a bit further in the theory and look into future research directions.

stat.ML↗

arXiv2019

Intra-day Equity Price Prediction using Deep Learning as a Measure of Market Efficiency

In finance, the weak form of the Efficient Market Hypothesis asserts that historic stock price and volume data cannot inform predictions of future prices. In this paper we show that, to the contrary, future intra-day stock prices could be predicted effectively until 2009. We demonstrate this using two different profitable machine learning-based trading strategies. However, the effectiveness of both approaches diminish over time, and neither of them are profitable after 2009. We present our implementation and results in detail for the period 2003-2017 and propose a novel idea: the use of such flexible machine learning methods as an objective measure of relative market efficiency. We conclude with a candidate explanation, comparing our returns over time with high-frequency trading volume, and suggest concrete steps for further investigation.

q-fin.TR↗

arXiv2019

Strategic Insider Trading Equilibrium with a Non-fiduciary Market Maker

The continuous-time version of Kyle's (1985) model is studied, in which market makers are not fiduciaries. They have some market power which they utilize to set the price to their advantage, resulting in positive expected profits. This has several implications for the equilibrium, the most important being that by setting a modest fee conditional of the order flow, the market maker is able to obtain a profit of the order of magnitude, and even better than, a perfectly informed insider. Our model also indicates why speculative prices are more volatile than predicted by fundamentals.

q-fin.TR↗

arXiv2019

Reinforcement Learning: Prediction, Control and Value Function Approximation

With the increasing power of computers and the rapid development of self-learning methodologies such as machine learning and artificial intelligence, the problem of constructing an automatic Financial Trading Systems (FTFs) becomes an increasingly attractive research topic. An intuitive way of developing such a trading algorithm is to use Reinforcement Learning (RL) algorithms, which does not require model-building. In this paper, we dive into the RL algorithms and illustrate the definitions of the reward function, actions and policy functions in details, as well as introducing algorithms that could be applied to FTFs.

q-fin.TR↗

arXiv2019

Automatic Financial Trading Agent for Low-risk Portfolio Management using Deep Reinforcement Learning

The autonomous trading agent is one of the most actively studied areas of artificial intelligence to solve the capital market portfolio management problem. The two primary goals of the portfolio management problem are maximizing profit and restrainting risk. However, most approaches to this problem solely take account of maximizing returns. Therefore, this paper proposes a deep reinforcement learning based trading agent that can manage the portfolio considering not only profit maximization but also risk restraint. We also propose a new target policy to allow the trading agent to learn to prefer low-risk actions. The new target policy can be reflected in the update by adjusting the greediness for the optimal action through the hyper parameter. The proposed trading agent verifies the performance through the data of the cryptocurrency market. The Cryptocurrency market is the best test-ground for testing our trading agents because of the huge amount of data accumulated every minute and the market volatility is extremely large. As a experimental result, during the test period, our agents achieved a return of 1800% and provided the least risky investment strategy among the existing methods. And, another experiment shows that the agent can maintain robust generalized performance even if market volatility is large or training period is short.

q-fin.TR↗