Final_1.pdf

Tying Up Loose Ends

In this section we highlight some issues of importance that were not covered
in the earlier discussions.

Multiple Thresholds Design

As mentioned earlier, the need for multiple threshold design arises when the
spread is generated using a mixture density white noise process. We could do
this by segmenting the time series sample based on periods or time of day.
The thresholds are then estimated for each sample. Subsequently, they are
checked to see if the difference between the values corresponding to the data
sets is significant. If it is, then we have multiple thresholds. Otherwise, we
stick to the single threshold approach. Note that in the case of multiple
thresholds there are inventory limits to be decided at each level, and the
problem is far from being solved in a conclusive manner.
An approach to circumvent multiple threshold design is to do the
threshold estimation in a dynamic fashion. The levels to apply currently are

Trading Design 135

FIGURE 8.7 Profit Profile Estimation.

Amount of Sigma Away from Mean

0.000.150.300.450.600.750.901.051.201.351.501.651.801.952.10

Profit Profile

0.00

0.05

0.10

0.15

0.20 Regularized Profit Profile

Raw Profit Profile