This paper develops a pairs trading framework based on a mean-reverting jump-diffusion model and applies it to minute-by-minute data of the S&P 500 oil companies from 1998 to 2015. The established statistical arbitrage strategy enables us to perform intraday and overnight trading. Essentially, we conduct a 3-step calibration procedure to the spreads of all pair combinations in a formation period. Top pairs are selected based on their spreads' meanreversion speed and jump behavior. Afterwards, we trade the top pairs in an out-of-sample trading period with individualized entry and exit thresholds. In the back-testing study, the strategy produces statistically and economically significant returns of 60.61 percent p.a. and an annualized Sharpe ratio of 5.30, after transaction costs. We benchmark our pairs trading strategy against variants based on traditional distance and time-series approaches and find its performance to be superior relating to risk-return characteristics. The mean-reversion speed is a main driver of successful and fast termination of the pairs trading strategy.

This study derives an optimal pairs trading strategy based on a Lévy-driven Ornstein-Uhlenbeck process and applies it to high-frequency data of the S&P 500 constituents from 1998 to 2015. Our model provides optimal entry and exit signals by maximizing the expected return expressed in terms of the first-passage time of the spread process. An explicit representation of the strategy's objective function allows for direct optimization without Monte Carlo methods. Categorizing the data sample into 10 economic sectors, we depict both the performance of each sector and the efficiency of the strategy in general. Results from empirical back-testing show strong support for the profitability of the model with returns after transaction costs ranging from 31.90 percent p.a. for the sector "Consumer Staples" to 278.61 percent p.a. for the sector "Financials". We find that the remarkable returns across all economic sectors are strongly driven by model parameters and sector size. Jump intensity decreases over time with strong outliers in times of high market turmoils. The value-add of our Lévy-based model is demonstrated by benchmarking it with quantitative strategies based on Brownian motion-driven processes.

This paper develops the regime classification algorithm and applies it within a fully-fledged pairs trading framework on minute-by-minute data of the S&P 500 constituents from 1998 to 2015. Specifically, the highly flexible algorithm automatically determines the number of regimes for any stochastic process and provides a complete set of parameter estimations. We demonstrate its performance in a simulation study-the algorithm achieves promising results for the general class of Lévy-driven Ornstein-Uhlenbeck processes with regime switches. In our empirical back-testing study, we apply our regime classification algorithm to propose a high-frequency pair selection and trading strategy. The results show statistically and economically significant returns with an annualized Sharpe ratio of 3.92 after transaction costs-results remain stable even in recent years. We compare our strategy with existing quantitative trading frameworks and find its results to be superior in terms of risk and return characteristics. The algorithm takes full advantage of its flexibility and identifies various regime patterns over time that are well-documented in the literature.

The use of stochastic differential equations offers great advantages for statistical arbitrage pairs trading. In particular, it allows the selection of pairs with desirable properties, e.g., strong mean-reversion, and it renders traditional rules of thumb for trading unnecessary. This study provides an exhaustive survey dedicated to this field by systematically classifying the large body of literature and revealing potential gaps in research. From a total of more than 80 relevant references, five main strands of stochastic spread models are identified, covering the ‘Ornstein–Uhlenbeck model’, ‘extended Ornstein–Uhlenbeck models’, ‘advanced mean-reverting diffusion models’, ‘diffusion models with a non-stationary component’, and ‘other models’. Along these five main categories of stochastic models, we shed light on the underlying mathematics, hereby revealing advantages and limitations for pairs trading. Based on this, the works of each category are further surveyed along the employed statistical arbitrage frameworks, i.e., analytic and dynamic programming approaches. Finally, the main findings are summarized and promising directions for future research are indicated.