Answer: 10.45%

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.

Author: Nikitesh Somanthe