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A singular stochastic control approach for optimal pairs trading with proportional transaction costs

Haipeng Xing

arXiv 24 Nov 2019 · Finance — Trading · publishedJournal of risk and financial management (2022) · 1 citations (OpenAlex)

arXiv:1911.10450 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Optimal trading strategies for pairs trading have been studied by models that try to find either optimal shares of stocks by assuming no transaction costs or optimal timing of trading fixed numbers of shares of stocks with transaction costs. To find optimal strategies which determine optimally both trade times and number of shares in pairs trading process, we use a singular stochastic control approach to study an optimal pairs trading problem with proportional transaction costs. Assuming a cointegrated relationship for a pair of stock log-prices, we consider a portfolio optimization problem which involves dynamic trading strategies with proportional transaction costs. We show that the value function of the control problem is the unique viscosity solution of a nonlinear quasi-variational inequality, which is equivalent to a free boundary problem for the singular stochastic control value function. We then develop a discrete time dynamic programming algorithm to compute the transaction regions, and show the convergence of the discretization scheme. We illustrate our approach with numerical examples and discuss the impact of different parameters on transaction regions. We study the out-of-sample performance in an empirical study that consists of six pairs of U.S. stocks selected from different industry sectors, and demonstrate the efficiency of the optimal strategy.

Citation extraction

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appendix boundary found by appendix_titled_section at “Appendix: Proof of Theorems” · 80% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1S. Mudchanatongsuk, J. Primbs, and W. Wong (2008) Optimal pairs trading: A stochastic approach0.87462100%
2E. Gatev, W. N. Goetzmann, and K. G. Rouwenhorst (2006) Pairs trading: Performance of a relative-value arbitrage rule0.84333100%
3Y. Lei and J. Xu (2015) Costly arbitrage through pairs trading0.73732100%
4M. Ngo and H. Pham (2016) Optimal switching for the pairs trading rule: A viscosity solutions approach0.73732100%
5G. Vidyamurthy (2004) Pairs Trading –- Quantitative Methods and Analysis0.64422100%
6D. Ehrman (2006) The Handbook of Pairs Trading: Strategies Using Equities, Options, and Futures0.40511100%
7R. Elliott, J. Van der Hoek, and W. Malcom (2005) Pairs trading0.40511100%
8T. Leung and X. Li (2015) Optimal mean reversion trading with transaction costs and stop-loss exit0.40511100%
9Q. Song and R. Yan (2013) An optimal pairs-trading0.40511100%
10A. Tourin and R. Yan (2013) Dynamic pairs trading using the stochastic control approach0.40511100%

Showing the top 10 of 14 scored citations.