Optimal trading strategies for Lévy-driven Ornstein–Uhlenbeck processes

ABSTRACT 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% p.a. for the sector ‘Consumer Staples’ to 278.61% 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 turmoil. The value-add of our Lévy-based model is demonstrated by benchmarking it with quantitative strategies based on Brownian motion-driven processes.

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