Financial Risk Manager Part 1

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The estimated standard error for a Monte Carlo simulation without antithetic variables is 4.21. The antithetic variables are now included so that the correlation between the pairs is 0.22 and the simulation is repeated 144 times. What is the percentage change in standard error?

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NNikitesh

Last updated: February 2, 2026 at 10:22

10.65%

46.65%

40.84%

10.45%

Explanation:

The standard error with antithetic variables is calculated using the formula:

$\frac{\sigma_g \sqrt{1 + \rho}}{\sqrt{b}}$

Given:

Original standard error without antithetic variables: $\frac{\sigma_g}{\sqrt{b}} = 4.21$
Correlation between pairs: $\rho = 0.22$
Number of simulations: $b = 144$

First, solve for $\sigma_g$ : $\sigma_g = 4.21 \times \sqrt{144} = 4.21 \times 12 = 50.52$

Then calculate the new standard error with antithetic variables: $\frac{50.52 \times \sqrt{1 + 0.22}}{\sqrt{144}} = \frac{50.52 \times \sqrt{1.22}}{12} = \frac{50.52 \times 1.1045}{12} = \frac{55.79}{12} = 4.65$

Finally, calculate the percentage change: $\frac{4.65}{4.21} - 1 = 1.1045 - 1 = 0.1045 = 10.45\%$

This matches option D.

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