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Paths for a target error

StatisticsMedium

A pilot run of $2500$ independent paths gives a sample standard deviation of $8$ for the payoff. How many paths in total give a standard error of $0.02$ ? Answer with a whole number.

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Hint

Standard error is the standard deviation over the square root of the path count.

Solution

The pilot's standard error is $\frac{8}{50} = 0.16$ , which is $\frac{0.16}{0.02} = 8$ times too large.
So the path count must grow by $8^{2} = 64$ times.
The total is $2500 \times 64 = 160000$ , so the answer is $160000$ .

Answer: $160000$

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