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The goal of cryptocurrencies is decentralization. In principle, all currencies have equal status. Unlike traditional stock markets, there is no default currency of denomination (fiat), thus the trading pairs can be set freely. However, it is impractical to set up a trading market between every two currencies. In order to control management costs and ensure sufficient liquidity, we must give priority to covering those…
This research aims to demonstrate a dynamic cointegration-based pairs trading strategy, including an optimal look-back window framework in the cryptocurrency market, and evaluate its return and risk by applying three different scenarios. We employ the Engle-Granger methodology, the Kapetanios-Snell-Shin (KSS) test, and the Johansen test as cointegration tests in different scenarios. We calibrate the mean-reversion sp…
We conduct a preliminary analysis of a pairs trading strategy using the Ornstein-Uhlenbeck (OU) process to model stock price spreads. We compare this approach to a naive pairs trading strategy that uses a rolling window to calculate mean and standard deviation parameters. Our findings suggest that the OU model captures signals and trends effectively but underperforms the naive model on a risk-return basis, likely due…
We propose a pairs trading model that incorporates a time-varying volatility of the Constant Elasticity of Variance type. Our approach is based on stochastic control techniques; given a fixed time horizon and a portfolio of two co-integrated assets, we define the trading strategies as the portfolio weights maximizing the expected power utility from terminal wealth. We compute the optimal pairs strategies by using a F…
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…
‘Pairs Trading’ is an investment strategy used by many Hedge Funds. Consider two similar stocks which trade at some spread. If the spread widens short the high stock and buy the low stock. As the spread narrows again to some equilibrium value, a profit results. This paper provides an analytical framework for such an investment strategy. We propose a mean-reverting Gaussian Markov chain model for the spread which is o…
We perform an extensive and robust study of the performance of three different pairs trading strategies—the distance, cointegration and copula methods—on the entire US equity market from 1962 to 2014 with time-varying trading costs. For the cointegration and copula methods, we design a computationally efficient two-step pairs trading strategy. In terms of economic outcomes, the distance, cointegration and copula meth…
We test a Wall Street investment strategy, “pairs trading,” with daily data over 1962–2002. Stocks are matched into pairs with minimum distance between normalized historical prices. A simple trading rule yields average annualized excess returns of up to 11% for self-financing portfolios of pairs. The profits typically exceed conservative transaction-cost estimates. Bootstrap results suggest that the “pairs” effect di…
Preface. Acknowledgments. PART ONE: BACKGROUND MATERIAL. Chapter 1. Introduction. The CAPM Model. Market Neutral Strategy. Pairs Trading. Outline. Audience. Chapter 2. Time Series. Overview. Autocorrelation. Time Series Models. Forecasting. Goodness of Fit versus Bias. Model Choice. Modeling Stock Prices. Chapter 3. Factor Models. Introduction. Arbitrage Pricing Theory. The Covariance Matrix. Application: Calculating…
Abstract This survey reviews the growing literature on pairs trading frameworks, i.e., relative‐value arbitrage strategies involving two or more securities. Research is categorized into five groups: The distance approach uses nonparametric distance metrics to identify pairs trading opportunities. The cointegration approach relies on formal cointegration testing to unveil stationary spread time series. The time‐series…
Abstract We examine the impact of trading costs on pairs trading profitability in the U.S. equity market, 1963 to 2009. After controlling for commissions, market impact, and short selling fees, pairs trading remains profitable, albeit at much more modest levels. Specifically, we document a risk‐adjusted return of about 30 basis points per month among portfolios of well‐matched pairs that are formed within refined ind…
This paper proposes an algorithmic trading framework integrating Environmental, Social, and Governance (ESG) ratings with a pairs trading strategy. It addresses the demand for socially responsible investment solutions by developing a unique algorithm blending ESG data with methods for identifying co-integrated stocks. This allows selecting profitable pairs adhering to ESG principles. Further, it incorporates technica…
Pairs trading is a family of trading techniques that determine their policies based on monitoring the relationships between pairs of assets. A common pairs trading approach relies on describing the pair-wise relationship as a linear Space State (SS) model with Gaussian noise. This representation facilitates extracting financial indicators with low complexity and latency using a Kalman Filter (KF), that are then proce…
Pairs trading is a strategy based on exploiting mean reversion in prices of securities. It has been shown to generate significant excess returns, but its profitability has dropped significantly in recent periods. We employ the most common distance and cointegration methods on US equities from 1990 to 2020 including the Covid-19 crisis. The strategy overall fails to outperform the market benchmark even with hyperparam…
With the recent rise of Machine Learning as a candidate to partially replace classic Financial Mathematics methodologies, we investigate the performances of both in solving the problem of dynamic portfolio optimization in continuous-time, finite-horizon setting for a portfolio of two assets that are intertwined. In Financial Mathematics approach we model the asset prices not via the common approaches used in pairs tr…
This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing r…
We consider the problem of optimal investment in a market with two cointegrated stocks and an agent with CRRA utility. We extend the findings of Liu and Timmermann [The Review of Financial Studies, 26(4):1048-1086, 2013] by paying special attention to when/if the associated stochastic control problem is well-posed and providing a verification result. Our new findings lead to a sharp well-posedness condition which is,…
We carry out a large-scale empirical data analysis to examine the efficiency of the so-called pairs trading. On the basis of relevant three thresholds, namely, starting, profit-taking, and stop-loss for the `first-passage process' of the spread (gap) between two highly-correlated stocks, we construct an effective strategy to make a trade via `active' stock-pairs automatically. The algorithm is applied to $1,784$ stoc…
BPE grows a vocabulary by repeatedly merging the most frequent adjacent pairs, starting from characters or bytes, until a target vocab size is reached.
CLIP jointly trains an image encoder and a text encoder so matched image–caption pairs are close in a shared space, enabling zero-shot visual classification by text prompts.
Contrastive learning pulls representations of related pairs together and pushes unrelated pairs apart. It is the pretraining idea behind SimCLR, CLIP, and many embedding models.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
A pip is the conventional smallest FX increment — usually 0.0001 for most pairs and 0.01 for JPY pairs.
Cointegration Pairs Trading — Mean-reversion on stationary spreads between related instruments.
Mean-revert spreads between country (or regional) ETFs that usually travel together — pairs at the index layer.
Trade a spread between two historically linked stocks when it is statistically wide, and unwind when it mean-reverts.
BPE grows a vocabulary by repeatedly merging the most frequent adjacent pairs, starting from characters or bytes, until a target vocab size is reached.
CLIP jointly trains an image encoder and a text encoder so matched image–caption pairs are close in a shared space, enabling zero-shot visual classification by text prompts.
Cointegration Pairs Trading — Mean-reversion on stationary spreads between related instruments.
Contrastive learning pulls representations of related pairs together and pushes unrelated pairs apart. It is the pretraining idea behind SimCLR, CLIP, and many embedding models.
FX Implied Volatility — Option-implied uncertainty for currency pairs, key for hedging and risk budgeting.
Mean-revert spreads between country (or regional) ETFs that usually travel together — pairs at the index layer.
Trade a spread between two historically linked stocks when it is statistically wide, and unwind when it mean-reverts.
A pip is the conventional smallest FX increment — usually 0.0001 for most pairs and 0.01 for JPY pairs.