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
Alpha signals for statistical arbitrage strategies are often driven by latent factors. This paper analyses how to optimally trade with latent factors that cause prices to jump and diffuse. Moreover, we account for the effect of the trader's actions on quoted prices and the prices they receive from trading. Under fairly general assumptions, we demonstrate how the trader can learn the posterior distribution over the latent states, and explicitly solve the latent optimal trading problem. We provide a verification theorem, and a methodology for calibrating the model by deriving a variation of the …
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into $k$ classes using the $k$-shell decomposition method. We investigate the influences of trading behaviors on the price impact by comparing a closed national market (A-shares) with an international market (B-shares), individuals and institutions, partially filled and filled trades, buyer-initiated and seller-initiated trades, a…
Few assets in financial history have been as notoriously volatile as cryptocurrencies. While the long term outlook for this asset class remains unclear, we are successful in making short term price predictions for several major crypto assets. Using historical data from July 2015 to November 2019, we develop a large number of technical indicators to capture patterns in the cryptocurrency market. We then test various classification methods to forecast short-term future price movements based on these indicators. On both PPV and NPV metrics, our classifiers do well in identifying up and down marke…
We employ both random forests and LSTM networks (more precisely CuDNNLSTM) as training methodologies to analyze their effectiveness in forecasting out-of-sample directional movements of constituent stocks of the S&P 500 from January 1993 till December 2018 for intraday trading. We introduce a multi-feature setting consisting not only of the returns with respect to the closing prices, but also with respect to the opening prices and intraday returns. As trading strategy, we use Krauss et al. (2017) and Fischer & Krauss (2018) as benchmark. On each trading day, we buy the 10 stocks with the highe…
Motivated by how transaction amount constrain trading volume and price volatility in stock market, we, in this paper, study the relation between volume and price if amount of transaction is given. We find that accumulative trading volume gradually emerges a kurtosis near the price mean value over a trading price range when it takes a longer trading time, regardless of actual price fluctuation path, time series, or total transaction volume in the time interval. To explain the volume-price behavior, we, in terms of physics, propose a transaction energy hypothesis, derive a time-independent trans…
Technical trading represents a class of investment strategies for Financial Markets based on the analysis of trends and recurrent patterns of price time series. According standard economical theories these strategies should not be used because they cannot be profitable. On the contrary it is well-known that technical traders exist and operate on different time scales. In this paper we investigate if technical trading produces detectable signals in price time series and if some kind of memory effect is introduced in the price dynamics. In particular we focus on a specific figure called supports…
In this paper we use fuzzy systems theory to convert the technical trading rules commonly used by stock practitioners into excess demand functions which are then used to drive the price dynamics. The technical trading rules are recorded in natural languages where fuzzy words and vague expressions abound. In Part I of this paper, we will show the details of how to transform the technical trading heuristics into nonlinear dynamic equations. First, we define fuzzy sets to represent the fuzzy terms in the technical trading rules; second, we translate each technical trading heuristic into a group o…
Price without transaction makes no sense. Trading volume authenticates its corresponding price, so there exist mutual information and correlation between price and trading volume. We are curious about fractal features of this correlation and need to know how structures in different scales translate information. To explore the influence of investment size (trading volume), price-wise (gain/loss), and time-scale effects, we analyzed the price and trading volume and their coupling by applying the MF-DXA method. Our results imply that price, trading volume, and price-volume coupling exhibit a powe…
Studying the micro-trading behaviors before stock price jumps is an important problem for financial regulations and investment decisions. In this study, we provide a new framework to study pre-jump trading behaviors based on multivariate time series analysis. Different from the existing literature, our methodology takes into account the temporal information embedded in the trading-related attributes and can better evaluate and compare the abnormality levels of different attributes. Moreover, it can explore the joint informativeness of the attributes as well as select a subset of highly informa…
We study the statistical properties of the recurrence intervals $τ$ between successive trading volumes exceeding a certain threshold $q$. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2009. Similar to the recurrence interval distribution of the price returns, the tail of the recurrence interval distribution of the trading volumes follows a power-law scaling, and the results are verified by the goodness-of-fit tests using the Kolmogorov-Smirnov (KS) statistic, t…
While market is a social field where information flows over the interacting agents, there have been not so many methods to observe the spreading information in the prices comprising the market. By incorporating the entropy transfer in information theory in its relation to the Granger causality, the paper proposes a tree of weighted directed graph of market to detect the changes of price might affect other price changes. We compare the proposed analysis with the similar tree representation built from the correlation coefficients of stock prices in order to have insight of possibility in seeing …
Due to the limited predictability of wind power and other stochastic generation, trading this energy in competitive electricity markets is challenging. This paper derives revenue-maximising and risk-constrained strategies for stochastic generators participating in electricity markets with a single-price balancing mechanism. Starting from the optimal---and impractical---strategy of offering zero or nominal power, which exposes the participant to potentially large imbalance costs, we develop a number of strategies that control risk by hedging against penalising balancing prices in favour of rewa…
A TGARCH modeling is argued to be the optimal basis for investigating the impact of index futures trading on spot price variability. We discuss the CSI-300 index (China-Shanghai-Shenzhen-300-Stock Index) as a test case. The results prove that the introduction of CSI-300 index futures (CSI-300-IF) trading significantly reduces the volatility in the corresponding spot market. It is also found that there is a stationary equilibrium relationship between the CSI-300 spot and CCSI-300-IF markets. A bidirectional Granger causality is also detected. ''Finally'', it is deduced that spot prices are pred…
Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock the clustering measure captures the degree of trading overlap among any two investors in that stock. We investigate the effect of crowded trades on stock price stability and show that market clustering has a causal effect on the properties of the tails of the stock return distribution, particularly the positive tail, even after controlling for commonly considered risk drivers. Reduced investor pool …
University of Cagliari（卡利亚里大学）；Brunel University（布鲁内尔大学）；University College London（伦敦大学学院）
This work aims to analyse the predictability of price movements of cryptocurrencies on both hourly and daily data observed from January 2017 to January 2021, using deep learning algorithms. For our experiments, we used three sets of features: technical, trading and social media indicators, considering a restricted model of only technical indicators and an unrestricted model with technical, trading and social media indicators. We verified whether the consideration of trading and social media indicators, along with the classic technical variables (such as price's returns), leads to a significati…
Trading volume movement prediction is the key in a variety of financial applications. Despite its importance, there is few research on this topic because of its requirement for comprehensive understanding of information from different sources. For instance, the relation between multiple stocks, recent transaction data and suddenly released events are all essential for understanding trading market. However, most of the previous methods only take the fluctuation information of the past few weeks into consideration, thus yielding poor performance. To handle this issue, we propose a graphbased app…
We study trade-based manipulation of stock prices from the perspective of complex trading networks constructed by using detailed information of trades. A stock trading network consists of nodes and directed links, where every trader is a node and a link is formed from one trader to the other if the former sells shares to the latter. Specifically, three abnormal network motifs are investigated, which are found to be formed by a few traders, implying potential intention of price manipulation. We further investigate the dynamics of volatility, trading volume, average trade size and turnover aroun…
We present a deep long short-term memory (LSTM)-based neural network for predicting asset prices, together with a successful trading strategy for generating profits based on the model's predictions. Our work is motivated by the fact that the effectiveness of any prediction model is inherently coupled to the trading strategy it is used with, and vise versa. This highlights the difficulty in developing models and strategies which are jointly optimal, but also points to avenues of investigation which are broader than prevailing approaches. Our LSTM model is structurally simple and generates predi…
Scuola Normale Superiore（比萨高等师范学校）；Consob（意大利国家证券监管委员会）；University College London（伦敦大学学院）
Identifying market abuse activity from data on investors' trading activity is very challenging both for the data volume and for the low signal to noise ratio. Here we propose two complementary unsupervised machine learning methods to support market surveillance aimed at identifying potential insider trading activities. The first one uses clustering to identify, in the vicinity of a price sensitive event such as a takeover bid, discontinuities in the trading activity of an investor with respect to his/her own past trading history and on the present trading activity of his/her peers. The second …
This research investigates efficiency on-line learning Algorithms to generate trading signals.I employed technical indicators based on high frequency stock prices and generated trading signals through ensemble of Random Forests. Similarly, Kalman Filter was used for signaling trading positions. Comparing Time Series methods with Machine Learning methods, results spurious of Kalman Filter to Random Forests in case of on-line learning predictions of stock prices
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 f…
In Part II of this paper, we concentrate our analysis on the price dynamical model with the moving average rules developed in Part I of this paper. By decomposing the excessive demand function, we reveal that it is the interplay between trend-following and contrarian actions that generates the price chaos, and give parameter ranges for the price series to change from divergence to chaos and to oscillation. We prove that the price dynamical model has an infinite number of equilibrium points but all these equilibrium points are unstable. We demonstrate the short-term predictability of the return…
This study proposes a scheme for stationarity analysis of stock price fluctuations based on KM$_2$O-Langevin theory. Using this scheme, we classify the time-series data of stock price fluctuations into three periods: stationary, non-stationary, and intermediate. We then suggest an example of a low-risk stock trading strategy to demonstrate the usefulness of our scheme by using actual stock index data. Our strategy uses a trend-based indicator, moving averages, for stationary periods and an oscillator-based indicator, psychological lines, for non-stationary periods to make trading decisions. Fi…
In Part III of this study, we apply the price dynamical model with big buyers and big sellers developed in Part I of this paper to the daily closing prices of the top 20 banking and real estate stocks listed in the Hong Kong Stock Exchange. The basic idea is to estimate the strength parameters of the big buyers and the big sellers in the model and make buy/sell decisions based on these parameter estimates. We propose two trading strategies: (i) Follow-the-Big-Buyer which buys when big buyer begins to appear and there is no sign of big sellers, holds the stock as long as the big buyer is still …
The increasing availability of "big" (large volume) social media data has motivated a great deal of research in applying sentiment analysis to predict the movement of prices within financial markets. Previous work in this field investigates how the true sentiment of text (i.e. positive or negative opinions) can be used for financial predictions, based on the assumption that sentiments expressed online are representative of the true market sentiment. Here we consider the converse idea, that using the stock price as the ground-truth in the system may be a better indication of sentiment. Tweets a…
We introduce a variant of the Barndorff-Nielsen and Shephard stochastic volatility model where the non Gaussian Ornstein-Uhlenbeck process describes some measure of trading intensity like trading volume or number of trades instead of unobservable instantaneous variance. We develop an explicit estimator based on martingale estimating functions in a bivariate model that is not a diffusion, but admits jumps. It is assumed that both the quantities are observed on a discrete grid of fixed width, and the observation horizon tends to infinity. We show that the estimator is consistent and asymptotical…
Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders' short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of price limit hits are not well studied partially due to the fact that main stock markets such as the US markets and most European markets do not set price limits. Here, we perform detailed analyses of the high-frequency data of all A-share common stocks traded on the Shanghai Stock E…
Employing a recent technique which allows the representation of nonstationary data by means of a juxtaposition of locally stationary patches of different length, we introduce a comprehensive analysis of the key observables in a financial market: the trading volume and the price fluctuations. From the segmentation procedure we are able to introduce a quantitative description of a group of statistical features (stylizes facts) of the trading volume and price fluctuations, namely the tails of each distribution, the U-shaped profile of the volume in a trading session and the evolution of the tradi…
We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. The basic method of our approach depends on the so-called renewal-reward theorem. Assuming that the stochastic process modelling the price change is a renewal process, we use the theorem to calculate the average waiting time of the process. The so-called ``inspec…
Pairs trading is a market-neutral strategy that exploits historical correlation between stocks to achieve statistical arbitrage. Existing pairs-trading algorithms in the literature require rather restrictive assumptions on the underlying stochastic stock-price processes and the so-called spread function. In contrast to existing literature, we consider an algorithm for pairs trading which requires less restrictive assumptions than heretofore considered. Since our point of view is control-theoretic in nature, the analysis and results are straightforward to follow by a non-expert in finance. To t…
The nature of fluctuations in the Indian financial market is analyzed in this paper. We have looked at the price returns of individual stocks, with tick-by-tick data from the National Stock Exchange (NSE) and daily closing price data from both NSE and the Bombay Stock Exchange (BSE), the two largest exchanges in India. We find that the price returns in Indian markets follow a fat-tailed cumulative distribution, consistent with a power law having exponent $α\sim 3$, similar to that observed in developed markets. However, the distributions of trading volume and the number of trades have a differ…
We use the expectation of the range of an arithmetic Brownian motion and the method of moments on the daily high, low, opening and closing prices to estimate the volatility of the stock price. The daily price jump at the opening is considered to be the result of the unobserved evolution of an after-hours virtual trading day.The annualized volatility is used to calculate Black-Scholes prices for European options, and a trading strategy is devised to profit when these prices differ flagrantly from the market prices.
Recent research on the response of stock prices to trading activity revealed long lasting effects, even across stocks of different companies. These results imply non-Markovian effects in price formation and when trading many stocks at the same time, in particular trading costs and price correlations. How the price response is measured depends on data set and research focus. However, it is important to clarify, how the details of the price response definition modify the results. Here, we evaluate different price response implementations for the Trades and Quotes (TAQ) data set from the NASDAQ s…
From electricity prices to profits: multidimensional probabilistic forecasting for BESS trading
organization= Department of Applied Mathematics, Wroc aw University of Science；organization= Department of Operations Research；Business Intelligence, Wroc aw University of Science
The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk forecasts: the probability of observing next day a large price movement is (super-universally) inversely proportional to the length of the ongoing low-variability period. Finally, a method is devised for a multi-factor scaling analysis. We apply the simplest, two-factor model to…
Distributions of assets returns exhibit a slight skewness. In this note we show that our model of endogenous price formation \cite{Reimann2006} creates an asymmetric return distribution if the price dynamics are a process in which consecutive trading periods are dependent from each other in the sense that opening prices equal closing prices of the former trading period. The corresponding parameter $α$ is estimated from daily prices from 01/01/1999 - 12/31/2004 for 9 large indices. For the S&P 500, the skewness distribution of all its constituting assets is also calculated. The skewness distrib…
Many studies assume stock prices follow a random process known as geometric Brownian motion. Although approximately correct, this model fails to explain the frequent occurrence of extreme price movements, such as stock market crashes. Using a large collection of data from three different stock markets, we present evidence that a modification to the random model -- adding a slow, but significant, fluctuation to the standard deviation of the process -- accurately explains the probability of different-sized price changes, including the relative high frequency of extreme movements. Furthermore, we…
We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Dt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a no…
