Optimal pairs trading rules and numerical methods
Luu, Phong Thanh
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Pairs trading involves two correlated securities. When divergence is underway, i.e., one stock moves up while the other moves down, a pairs trade is entered consisting of a short position in the outperforming stock and long position in the underperforming one. Such a strategy bets the ``spread" between the two would eventually converge. The main advantage of pairs trading is its risk neutral nature, i.e., it can be profitable regardless the general market condition. In this dissertation, a difference of the pair is studied. When the difference is governed by a mean-reversion model, the trade will be closed whenever the difference reaches a target level or a pre-determined cutloss limit. On the other hand, when it satisfies a regime-switching model, the trade will be determined by two conditional probability threshold levels. The objective is to identify the optimal threshold levels so as to maximize an overall return. We apply stochastic control theories to solve these optimal pairs trading problems. Many techniques have been implemented, including ordinary differential equation, stochastic approximation, and viscosity solution approaches. The effectiveness of these methods is examined in numerical examples. Index words: Geometric Brownian motion, mean reversion model, regime switching model, HJB equation, stochastic approximation, viscosity solution.