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Q.12 The estimated standard error for a Monte Carlo simulation without antithetic variables is 3.65. The antithetic variables are now included so that the correlation between the pairs is -0.65 and the simulation is repeated 100 times. What is the percentage change in standard error? | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

Recall that the standard error of the simulation when antithetic variables are included expectation is given by:

\frac{\sigma_g \sqrt{1 + p}}{\sqrt{b}}

We are told that,

\frac{\sigma_g}{b} = 3.65 \Rightarrow \sigma_g = 3.65 \times \sqrt{100} = 36.5

So the new standard error is given by:

\frac{\sigma_g \sqrt{1 + p}}{\sqrt{b}} = \frac{36.5 \times \sqrt{1 - 0.65}}{\sqrt{100}} = 2.1593

So the percentage change is:

\frac{2.1593}{3.65} - 1 = -40.84\%

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Q.12 The estimated standard error for a Monte Carlo simulation without antithetic variables is 3.65. The antithetic variables are now included so that the correlation between the pairs is -0.65 and the simulation is repeated 100 times. What is the percentage change in standard error?

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