Statistical Arbitrage Strategies Research Articles

Relationship between deep hedging and delta hedging: Leveraging a statistical arbitrage strategy

In this study, we explore the links between deep hedging and delta hedging using a statistical arbitrage strategy. Specifically, we show that hedging that minimizes loss risk combines delta hedging with a statistical arbitrage strategy. The numerical experiments in a simple Black–Scholes world also verify these results. Moreover, it is known that the existence of statistical arbitrages can hamper proper learning of deep hedging. For this problem, the obtained relationship and analysis of the profit and loss (PnL) distribution of deep hedging provide us with insight into risk measures that are resistant to statistical arbitrages. We conclude that the use of these robust risk measures allows us to ignore the estimation of drift terms in asset price processes.

Deep reinforcement learning applied to statistical arbitrage investment strategy on cryptomarket

In the complex and dynamic nature of financial markets where increasingly sophisticated investment strategies are required, deep reinforcement learning (DRL) has proven successful in generating real-time investment strategies, outperforming classical models. Alongside this, statistical arbitrage strategies exploit temporary market inefficiencies to generate returns. In this regard, a novel DRL-based arbitrage method has been developed.This paper presents a unified framework that combines classical statistical arbitrage theory with DRL framework to generate investment strategies. The framework addresses the challenges of identifying similar asset portfolios, extracting signals indicating temporary price deviations, and determining optimal trading rules given market conditions. The proposed methodology involves constructing arbitrage portfolios based on cointegration relationships, removing signals from price series and portfolios, and using a DRL agent to make optimal decisions within a fixed time horizon.The empirical analysis focuses on the cryptocurrency market, known for its volatility and risk. Results demonstrate that DRL agents can generate strategies with positive returns in out-of-sample periods 79.52% to 112.82% with no transaction cost, outperforming market benchmark Bitcoin 32.51% return, the best performing over the period Litecoin with 57.11% return and the worst performing Solana with a 35.70% loss. Moreover, these strategies effectively reduce risk, achieving higher risk-adjusted returns on individual assets. The strategies maintain positive returns when considering transaction costs, with the DRL agent outperforming the standard arbitrage strategy. The best-performing strategy is based on a Deep Q-Network (DQN) agent with a return of 18.39%, annualized volatility of 12.22%, and an annualized Sharpe ratio of 2.43. At the same time, Bitcoin holds an annualized volatility of 44.13% and a Sharpe ratio of 1.08.Their randomness and coherence are studied to verify the robustness of the agents’ decisions. The actions generated by the agents are not random but based on well-founded policies, which align with the obtained results.

Pairs trading in the index options market

We test the Index options market efficiency by means of a statistical arbitrage strategy, i.e. pairs trading. Using data on five Index Option Markets of the Euro Area, we first identify any potential option mispricing based on deviations from the long-run relationship linking their implied volatilities. Then, we evaluate the profitability of a simple pair trading strategy on the mispriced options. Despite the fact that the signals of potential mispricing are frequent, the statistical arbitrage does not produce significant profits, thus providing evidence in support of Index Option market efficiency. The results, which remain unchanged in a variety of robustness checks, also prove that the observed profits are strongly associated to the moneyness of the options traded while they do not correlate to options’ maturity or to financial market turbulence.

Exploring arbitrage opportunities between China's carbon markets based on statistical arbitrage pairs trading strategy

Pairs trading is one of the mainstream statistical arbitrage strategies in current financial market practice that can seize possible arbitrage opportunities caused by mispricing between similar assets. Based on the theory of statistical arbitrage and the similar attributes of carbon emission allowances traded in different carbon markets, this paper studies the applicability of the pairs trading strategy among different pilot markets in China. The novelty and possible contribution of this paper are as follows. Firstly, this paper extends the statistical arbitrage-based pairs trading framework to the analysis of carbon market transactions in China, which broadens the understanding of the correlation between China's carbon markets. Secondly, this study explores the arbitrage opportunities among China's regional carbon markets that have not been revealed by previous studies. Thirdly, based on the pairs trading analytical model adopted in this study, this paper further investigates the operation characteristics of China's carbon markets and the interaction between markets, as the sensitivity of strategy performance to the key parameters is also discussed. The results show that arbitrage based on pairs trading is profitable. In the baseline case, the annualized arbitrage returns between the Shanghai emission allowance and Beijing emission allowance is about 9.11%, the highest among all pairs. However, there is almost no pairing relationship between the Tianjin carbon market and other markets. By discussing the time distribution of arbitrage signals generated by the pairs trading strategy, it is found that most signals are sent out during the inactive trading period in a compliance cycle. The conclusions provide valuable insights for formulating relevant carbon market regulatory policies and investors' participation in arbitrage activities in China's carbon trading markets.

Relationship between deep hedging and delta hedging: leveraging a statistical arbitrage strategy

Relationship between deep hedging and delta hedging: leveraging a statistical arbitrage strategy

Predicting Chinese Commodity Futures Price: An EEMD-Hurst-LSTM Hybrid Approach

This paper proposes an EEMD-Hurst-LSTM prediction method based on the ensemble learning framework, which is applied to the prediction of typical commodities in China’s commodity futures market. This method performs ensemble empirical mode decomposition (EEMD) on commodity futures prices, and incorporates the components obtained by EEMD decomposition and the adaptive fractal Hurst index calculated by using intraday high-frequency data as new features into the LSTM model to decompose its correlation with the external market to detect changes in market conditions. The results show that the EEMD-Hurst-LSTM method has better predictive performance compared to other horizontal single models and longitudinal deep learning combined models. Meanwhile, the trading strategy designed according to this ensemble model can obtain more returns than other trading strategies and have the best risk control level. The research of this paper provides important implications for the trend following of commodity markets and the investment risk management of statistical arbitrage strategies.

Statistical Arbitrage for Multiple Co-integrated Stocks.

In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton–Jacobi–Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high.Supplementary InformationThe online version contains supplementary material available at 10.1007/s00245-022-09838-3.

A Cointegration Approach for Selection of Currency Pairs

Pairs trading is a statistical arbitrage strategy based on the construction of mean reversion in prices of securities. While these strategies tend to perform well in equities, their effectiveness and performance in the currency market is yet to be tested, which is generally inefficient and predictable. The purpose of this study was to select the pairs for pairs trading in the forex market of select currencies: EUR/USD, GBP/USD, USD/CAD, USD/INR, USD/JPY, and USD/NZD during the period starting from October 1, 2010 – October 20, 2020. The research was organized into three parts to determine the possible pairs of six currencies over different time periods. First, the closeness of potential pairs of six currencies was established using the distance approach for 10 years, 5 years, and 2 years. After that, the Engle – Granger two-step test for cointegration was applied to examine the validity of the top 10 closest pairs of currencies for pairs trading in the study. Based on the empirical results of the cointegration approach, we found very few good pairs in the forex market in our study. USD_INR/USD_NZD was found to be statistically significant at a 10% level of significance over the 10-year sample period, and the same pair of currencies was also found to be statistically significant over a 5-year sample period, but this pair was not found to be statistically significant in the 2-year sample period; whereas, USD_JPY/USD_NZD was found to be statistically significant in the 2 - year period at a 10% level of significance.

Pairs Trading Strategy for A and H Shares Based on Kalman-HMM Approach

Pairs trading is a statistical arbitrage strategy that takes advantage of unbalanced financial markets. A common difficulty for quantitative trading participants is the detection of market institutional changes in financial markets. In order to solve this issue, the hidden Markov model (HMM) is applied for status detection. The research objective is to use Kalman filter to predict and the hidden Markov model (HMM) to identify state transitions on the basis of screening transaction pairs with obvious co-integration relationship. This research would prove the profitability of the strategy and the ability to resist risk through the combination of these two methods with real data. The empirical results showed that compared with the traditional cointegration strategy, the holding yield increased from 1.6% to 16.2% and the maximum pullback reduced to 0.02%. Further research is required to improve trading rules.

Structural break-aware pairs trading strategy using deep reinforcement learning.

Pairs trading is an effective statistical arbitrage strategy considering the spread of paired stocks in a stable cointegration relationship. Nevertheless, rapid market changes may break the relationship (namely structural break), which further leads to tremendous loss in intraday trading. In this paper, we design a two-phase pairs trading strategy optimization framework, namely structural break-aware pairs trading strategy (SAPT), by leveraging machine learning techniques. Phase one is a hybrid model extracting frequency- and time-domain features to detect structural breaks. Phase two optimizes pairs trading strategy by sensing important risks, including structural breaks and market-closing risks, with a novel reinforcement learning model. In addition, the transaction cost is factored in a cost-aware objective to avoid significant reduction of profitability. Through large-scale experiments in real Taiwan stock market datasets, SAPT outperforms the state-of-the-art strategies by at least 456% and 934% in terms of profit and Sortino ratio, respectively.

Machine Learning in Futures Markets

In this paper, we demonstrate how a well-established machine learning-based statistical arbitrage strategy can be successfully transferred from equity to futures markets. First, we preprocess futures time series comprised of front months to render them suitable for our returns-based trading framework and compile a data set comprised of 60 futures covering nearly 10 trading years. Next, we train several machine learning models to predict whether the h-day-ahead return of each future out- or underperforms the corresponding cross-sectional median return. Finally, we enter long/short positions for the top/flop-k futures for a duration of h days and assess the financial performance of the resulting portfolio in an out-of-sample testing period. Thereby, we find the machine learning models to yield statistically significant out-of-sample break-even transaction costs of 6.3 bp—a clear challenge to the semi-strong form of market efficiency. Finally, we discuss sources of profitability and the robustness of our findings.

Pairs Trading In The index Options Market

We test the Index options market efficiency by means of a statistical arbitrage strategy, i.e. pairs trading. Using data on five Stock Indexes of the Euro Area, we first identify any potential option mispricing based on deviations from the long-run relationship linking their implied volatilities. Then, we evaluate the profitability of a simple pair trading strategy on the mispriced options. Despite the signals of potential mispricing are frequent, the statistical arbitrage does not produce significant positive returns, thus providing evidence in support of Index Option market efficiency. The time-to-maturity of the options involved in the trade as well as financial market turbulence have a marginal effect on the eventual strategy returns, which are instead mostly driven by the moneyness of the options traded. Our results remain qualitatively unchanged if a stricter definition of reversion to the equilibrium is applied or when the long-run relationship is estimated on an (artificially derived) time series of options prices rather than on options’ implied volatilities.

Deep Reinforcement Learning for Algorithmic Trading

We employ reinforcement learning (RL) techniques to devise statistical arbitrage strategies in electronic markets. In particular, double deep Q network learning (DDQN) and a new variant of reinforced deep Markov models (RDMMs) are used to derive the optimal strategies for an agent who trades in a foreign exchange (FX) triplet. An FX triplet consists of three currency pairs where the exchange rate of one pair is redundant because, by no-arbitrage, it is determined by the exchange rates of the other two pairs. We use simulations of a co-integrated model of exchange rates to implement the strategies and show their financial performance.

High-frequency Statistical Arbitrage Strategy Based on Stationarized Order Flow Imbalance

From a high-frequency perspective, the order book data records each market participant’s price expectations for the current underlying assets, and therefore it records the fundamental mechanism of pricing. In this paper, we propose a stationarized indicator based on the classical indicator – Order Flow Imbalance (OFI), and empirically find that there is a stronger linear relationship between the new indicator and the mid-price. Furthermore, we develop a statistical arbitrage strategy based on this new indicator. Compared with the classic indicator, the strategy built with the new indicator has better performance.

Option Pricing Incorporating Factor Dynamics in Complete Markets

Using the Donsker–Prokhorov invariance principle, we extend the Kim–Stoyanov–Rachev–Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the Cherny–Shiryaev–Yor invariance principles, we formulate a new binomial path-dependent pricing model for discrete- and continuous-time complete markets where the stock price dynamics depends on the log-return dynamics of a market influencing factor. In the discrete case, we extend the results of this new approach to a financial market with informed traders employing a statistical arbitrage strategy involving trading of forward contracts. Our findings are illustrated with numerical examples employing US financial market data. Our work provides further support for the conclusion that any option pricing model must preserve valuable information on the instantaneous mean log-return, the probability of the stock’s upturn movement (per trading interval), and other market microstructure features.

Robust Statistical Arbitrage Strategies

We investigate statistical arbitrage strategies when there is ambiguity about the underlying time-discrete financial model. Pricing measures are assumed to be martingale measures calibrated to prices of liquidly traded options, whereas the set of admissible physical measures is not necessarily implied from market data. Our investigations rely on the mathematical characterization of statistical arbitrage, which was originally introduced by Bondarenko in 2003. In contrast to pure arbitrage strategies, statistical arbitrage strategies are not entirely risk-free, but the notion allows to identify strategies which are profitable on average, given the outcome of a specific sigma-algebra. Besides a characterization of robust statistical arbitrage, we also provide a super-/sub-replication theorem for the construction of statistical arbitrage strategies based on path-dependent options. In particular, we show that the range of statistical arbitrage-free prices is, in general, much tighter than the range of arbitrage-free prices.

Robust statistical arbitrage strategies

We investigate statistical arbitrage strategies when there is ambiguity about the underlying time-discrete financial model. Pricing measures are assumed to be martingale measures calibrated to prices of liquidly traded options, whereas the set of admissible physical measures is not necessarily implied from market data. Our investigations rely on the mathematical characterization of statistical arbitrage, which was originally introduced by Bondarenko [Statistical arbitrage and securities prices. Rev. Financ. Stud., 2003, 16, 875–919]. In contrast to pure arbitrage strategies, statistical arbitrage strategies are not entirely risk-free, but the notion allows one to identify strategies which are profitable on average, given the outcome of a specific σ-algebra. Besides a characterization of robust statistical arbitrage, we also provide a super-/sub-replication theorem for the construction of statistical arbitrage strategies for path-dependent options. In particular, we show that the range of statistical arbitrage-free prices is, in general, much tighter than the range of arbitrage-free prices.

Separating the signal from the noise – Financial machine learning for Twitter

Most statistical arbitrage strategies in the academic literature solely rely on price time series. By contrast, alternative data sources are of growing importance for professional investors. We contribute to bridging this gap by assessing the price-predictive value of millions of tweets on intraday returns of the S&P 500 constituents from 2014 and 2015. For this purpose, we design a machine learning system addressing specific challenges inherent to this task. At first, building on the literature of financial dictionaries, we engineer domain-specific features along three categories, i.e., directional indicators, relevance indicators and meta features. Next, we leverage a random forest to extract the relationship between these features and subsequent stock returns in a low signal-to-noise setting. For performance evaluation, we run a rigorous event-based backtesting study across all tweets and stocks. We find annualized returns of 6.4 percent and a Sharpe ratio of 2.2 after transaction costs. Finally, we illuminate the machine learning black box and unveil sources of profitability: First, results are both driven and limited by the temporal clustering of tweets, i.e., the majority of profits stem from tweets clustered closely together in time, corresponding to high-event situations. Second, the importance of included features follows an economic rationale, e.g., tweets with positive sentiment tend to yield positive returns and vice versa. Third, we find that stocks of medium market capitalization and from the consumer and technology sectors contribute most to our results, which we interpret as a trade-off between tweet coverage and tweet relevance.

Statistical Arbitrage Strategy in Multi-Asset Market Using Time Series Analysis

The statistical arbitrage strategy is one of the most traditional investment strategies. There are many theoretical and empirical studies until now. However, almost all of the statistical arbitrage strategies focus on the price difference (spread) between two similar assets in the same asset class and exploit the mean reversion of spreads, i.e. pairs trading. In this study, we extend the strategy to multiple assets in the multi-asset market. Although mean-reverting portfolios were derived based on a single criterion in related researches, we derive a mean-reverting portfolio by optimizing multiple mean-reversion criteria. We expect that a mean-reverting portfolio based on multiple indicators leads to a higher return/risk. We perform an empirical analysis in multi-asset market and show the profitability of our strategy.

Excursion Risk

The risk and return profiles of a broad class of dynamic trading strategies, including pairs trading and other statistical arbitrage strategies, may be characterized in terms of excursions of the market price of a portfolio away from a reference level. We propose a mathematical framework for the risk analysis of such strategies, based on a description in terms of price excursions, first in a pathwise setting, without probabilistic assumptions, then in a Markovian setting. We introduce the notion of delta-excursion, defined as a path which deviates by delta from a reference level before returning to this level. We show that every continuous path has a unique decomposition into delta-excursions, which is useful for the scenario analysis of dynamic trading strategies, leading to simple expressions for the number of trades, realized profit, maximum loss and drawdown. As delta is decreased to zero, properties of this decomposition relate to the local time of the path. When the underlying asset follows a Markov process, we combine these results with Ito's excursion theory to obtain a tractable decomposition of the process as a concatenation of independent delta-excursions, whose distribution is described in terms of Ito's excursion measure. We provide analytical results for linear diffusions and give new examples of stochastic processes for flexible and tractable modeling of excursions. Finally, we describe a non-parametric scenario simulation method for generating paths whose excursion properties match those observed in empirical data.