The most useful feature used in finance of the Ornstein-Uhlenbeck (OU) stochastic process is its mean-reverting property: the OU process tends to drift towards its long- term mean (its equilibrium state) over time. This important feature makes the OU process arguably the most popular statistical model for developing best pair-trading strategies. However, optimal strategies depend crucially on the first passage time (FPT) of the OU process to a suitably chosen boundary and its probability density is not analytically available in general. Even for crossing a simple constant boundary, the FPT of the OU process would lead to crossing a square root boundary by a Brownian motion process whose FPT density involves the complicated parabolic cylinder function. To overcome the limitations of the existing methods, we propose a novel class of non-linear boundaries for obtaining optimal decision thresholds. We prove the existence and uniqueness of the maximizer of our decision rules. We also derive simple formulas for some FPT moments without analytical expressions of its density functions. We conduct some Monte Carlo simulations and analyze several pairs of stocks including Coca-Cola and Pepsi, Target and Walmart, Chevron and Exxon Mobil. The results demonstrate that our method outperforms the existing procedures.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc1873709 |
| Date | 12 1900 |
| Creators | Tamakloe, Emmanuel Edem Kwaku |
| Contributors | Song, Kai-Sheng, Iaia, Joseph A., Trang, Nam |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | xviii, 147 pages : illustrations (some color), Text |
| Rights | Public, Tamakloe, Emmanuel Edem Kwaku, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved. |
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