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  1. 2 Managerial Economics

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  1. 1 Endres S.

  2. 1 Rende J.

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  1. 2 2019

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Review of stochastic differential equations in statistical arbitrage pairs trading

100%
Endres S.
Managerial Economics
|
2019
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vol. 20
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issue 2
71-118
EN
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 meanreversion, 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 fur future research are indicated.
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Pairs trading with the persistence-based decomposition model

86%
Rende J.
Managerial Economics
|
2019
|
vol. 20
|
issue 2
151-180
EN
Recently, the persistence-based decomposition (PBD) model has been introduced to the scientific community by Rende et al. (2019). It decomposes a spread time series between two securities into three components capturing infinite, finite, and no shock persistence. The authors provide empirical evidence that the model adopts well to noisy high-frequency data in terms of model fitting and prediction. We put the PBD model to test on a large-scale high-frequency pairs trading application, using S&P 500 minute-by-minute data from 1998 to 2016. After accounting for execution limitations (waiting rule, volume constraints, and short-selling fees) the PBD model yields statistically significant and economically meaningful annual returns after transaction costs of 9.16 percent. These returns can only partially be explained by the exposure to common risk. In addition, the model is superior in terms of risk-return metrics. The model performs very well in bear markets. We quantify the impact of execution limitations on risk and return measures by relaxing backtesting restrictions step-by-step. If no restrictions are imposed, we find annual returns after costs of 138.6 percent.
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