Optimal Pair-Trading Decision Rules for a Class of Non-Linear Boundary Crossings by Ornstein-Uhlenbeck Processes Page: 86
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5.2.3.3. Monte Carlo Simulation
We also perform a Monte Carlo simulation with on the same parameter values as
above to see the average estimate of the methods. From the results in table 5.14, we see
that on average all the parameters are well estimated and there is significant improve in the
estimates for b in comparison with the case of one realization. A plot of the paths generated
from these estimates in comparison with the true path can be found in figure 5.28.
True Value Method Estimate Bias Standard Error RMSE
MLE 0.00019993 -0.00000007 0.00000290 0.00000000
a 0.00020000
LS 0.00020000 -0.00000000 0.00000478 0.00000000
MLE 0.02083869 0.00083869 0.02720594 0.00074087
b 0.02000000
LS 0.02017871 0.00017871 0.04493147 0.00201887
MLE 0.08344855 0.00344855 0.01285059 0.00017703
A 0.08000000
LS 0.08481821 0.00481821 0.01221014 0.00017230
MLE 0.00500934 0.00000934 0.00010678 0.00000001
- 0.00500000
LS 0.00500355 0.00000355 0.00010317 0.00000001
TABLE 5.14. Performance of Maximum Likelihood and Least Squares meth-
ods for estimating the trend-stationary OU parameters, by 10,000 Monte Carlo
simulations, using a path of length 1260
5.2.4. Short Path
Let us now consider short term trade time horizon.
5.2.4.1. Generating the Spread
We will use the last 126 steps of the path presented in figure 5.25. A graph of this
path can be found in figure 5.29.86
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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/m1/105/: accessed July 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; .