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

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Document pages: 39 pages

Abstract: Optimal trading strategies for pairs trading have been studied by models thattry to find either optimal shares of stocks by assuming no transaction costs oroptimal timing of trading fixed numbers of shares of stocks with transactioncosts. To find optimal strategies which determine optimally both trade timesand number of shares in pairs trading process, we use a singular stochasticcontrol approach to study an optimal pairs trading problem with proportionaltransaction costs. Assuming a cointegrated relationship for a pair of stocklog-prices, we consider a portfolio optimization problem which involves dynamictrading strategies with proportional transaction costs. We show that the valuefunction of the control problem is the unique viscosity solution of a nonlinearquasi-variational inequality, which is equivalent to a free boundary problemfor the singular stochastic control value function. We then develop a discretetime dynamic programming algorithm to compute the transaction regions, and showthe convergence of the discretization scheme. We illustrate our approach withnumerical examples and discuss the impact of different parameters ontransaction regions. We study the out-of-sample performance in an empiricalstudy that consists of six pairs of U.S. stocks selected from differentindustry sectors, and demonstrate the efficiency of the optimal strategy.

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