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.