Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 13
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horizon due to reduction in deviation from the long term mean over time. It is worth noting
that this phenomenon is very common, but we only picked a few instances for each of the
four pairs to make our point as shown in figures 2.2, 2.3, 2.4 and 2.5.
2.3.3. Zeng and Leng's Strategy and Transaction Cost
Except for Goncu and Akyildirim's strategy, most known pairs trading strategies de-
pend on transaction cost. In fact Zeng and Lee stated in their paper that at zero transaction
cost their result yield the same maximal return as the conventional method [40]. On top of
this we found out that a zero transaction cost would mean a threshold of zero for Zeng and
Lee's method. This can be checked by solving equation 80. However, trades nowadays have
either zero or close to zero transaction cost, which means Zeng and Lee's strategy would not
be applicable in such circumstances.
2.3.4. A Discussion on the Method of Goncu and Akyildirim
As stated earlier Goncu and Akyildirim's method is based on the investment time
horizon, T. The function they sought to maximize is:
I T2 ce-t (c2e-2t
P(T < T) = (exP 2 2t)dt
S (1 - e-2)3/2 2 -t
We show a plot of this function for the case of T = 0.5 in figure 2.6. It is clear from
this plot that the optimal value of the function is obtained when c is approximately equal
to zero, which makes intuitive sense, in that the closer the threshold is to the long term
mean, the higher the chance of reaching it within the time horizon T. But this would
mean their threshold is essentially zero, hence provides no trade opportunity in the given
time horizon. So, the strategy fails. Besides this, we also have concerns regarding the
optimization technique employed by the authors in arriving at the optimal expression for
level c. The approach does not guarantee in general that P(T) is a probability function for
the resulting value of c. We also note that for large time horizon T, say T = 2, the resulting
thresholds for their strategy are too far from the spread to yield any trades at all. We show
an example in figure 2.7 for 2-year time horizon for the German utility companies EOAN
and RWE.13
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Tamakloe, Emmanuel Edem Kwaku. Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes, dissertation, December 2021; Denton, Texas. (https://digital.library.unt.edu/ark:/67531/metadc1873709/m1/32/?rotate=0: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .