Final_1.pdf

Let us now attempt to explain the reason why we obtain such a noisy es-
timate for the profit profile. Note that we have a fine level of discretization
that is coupled with a small sample size. This has led to a step function form
for the count function, which in reality is expected to be monotonically de-
creasing. Also, notice that whenever we hit a step, the profit profile kinks
upward. We shall term this the discretization effect. To obtain a frequency
count that is monotonically decreasing, we would need to correct for this
discretization effect. We can correct for the discretization effect and ensure
a monotonically decreasing function by performing a simple linear interpo-
lation between the points constituting the two levels in the step function. To
show what we mean, look at Figure 8.4.
After this adjustment, even though the count is monotonically decreas-
ing, it is still not smooth. The solution we propose to overcome this is widely

Trading Design 129

FIGURE 8.2A Probability Estimates from Counts.

Sigma Away from Mean

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.0

Probability

0.1

0.2

0.3

0.4

0.5

FIGURE 8.2B Profits Levels.

Sigma Away from Mean

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Profit

0.0

0.5

1.0

1.5

2.0