Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 74
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Substituting the time horizon T = 5 into the corresponding h(f, ,) in chapter 4 and
solving gives the optimizer as (3, 5) (1.3351, 0.1856), approximated to four decimal places.
Thus the optimal thresholds for this case are:
S(t) ft# + ~(1.3351e- t - 0.1856elt).
V2Taking the estimates of the OU process parameters to be ft = 1.5020, A
a = 0.0135, as in case 1, we approximate the optimal thresholds as:0.0602 and
0.0135 0o sz
g(t) 1.5020 + 0.015 (1.3351e-0.06O2t' - 0.1856e ' )
2(0.0602)
= 1.5020 + 0.0389(1.3351e-0.0602t - 0.1856eo.0602t)A graphical representation of this result is shown in figure 5.21.
P~Q1.6-
1.5-
1.4-
0
500
1000
Days
FIGURE 5.21. New threshold case 2 on the OU representation of the spread
of length 1260 between ln(Qt) and ln(Pt)74
(53)
D)
0~
Q/Key
- - Long-term mean
- Spread
- Case 2 threshold
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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/m1/93/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .