Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 75
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In contrast, the optimal thresholds provided by case 1 has a narrower band in com-
parison with that of case 2 and as such is crossed more often by the path and hence generates
more trades, while the optimal threshold presented in case 2 has a broader band, and as a
result may have fewer number of crossings than case 1 and therefore fewer number of trades,
but due to the wide band, the return per trade cycle is greater for case 2 than case one.
5.1.6.4. Short Path
Let us now look at the situation for short trade time horizons. Specifically, we consider
126 days or half a year. From table 5.12 , we see that apart from A, the other two parameters
were quite well estimated. Nonetheless, a look at the graph in figure 5.22 shows that the
true path is quite well approximated by our estimated path.
True Value Method Estimate Bias Standard Error RMSE
MLE 1.50027460 0.00027460 0.01057400 0.00011189
p 1.50000000
LS 1.50028069 0.00028069
MLE 0.12241420 0.07241420 0.04302880 0.00709529
A 0.05000000
LS 0.12250859 0.07250859
MLE 0.01438200 0.00138200 0.00095680 0.00000283
- 0.01300000
LS 0.01444111 0.00144111
TABLE 5.12. One realization of parameter estimates by maximum likelihood
and least squares methods, for the OU representation of the spread of length
126 between ln(Qt) and ln(Pt)
5.1.6.5. Case 1: -= 0
Substituting the time horizon T =2 into the corresponding h(8) in chapter 4 and
solving gives the optimizer of the expected return as /3 0.8735, approximated to four
decimal places.75
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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/m1/94/?rotate=90: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .