An Optimal Pairs-Trading Rule
AbstractThis paper is concerned with a pairs trading rule. The idea is to monitor two historically correlated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered which consists of a pair to short the outperforming stock and to long the underperforming one. Such a strategy bets the "spread" between the two would eventually converge. In this paper, a difference of the pair is governed by a mean-reverting model. The objective is to trade the pair so as to maximize an overall return. A fixed commission cost is charged with each transaction. In addition, a stop-loss limit is imposed as a state constraint. The associated HJB equations (quasi-variational inequalities) are used to characterize the value functions. It is shown that the solution to the optimal stopping problem can be obtained by solving a number of quasi-algebraic equations. We provide a set of sufficient conditions in terms of a verification theorem. Numerical examples are reported to demonstrate the results.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1302.6120.
Date of creation: Feb 2013
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-02 (All new papers)
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