Financial Risk Manager Part 1

The correct answer is D) All the above.

Explanation:

1. Option A is correct: Antithetic variates reduce sampling error by introducing negative correlation between pairs of simulation runs. This correlation helps to reduce the variance of the estimator.

2. Option B is correct: The antithetic variates method indeed involves taking the complement (or negative) of each random draw (e.g., if u is a uniform random variable, using 1-u as the antithetic variate) and then repeating the simulation with these antithetic values.

3. Option C is correct: The primary purpose of antithetic variates is to reduce the variance of simulation results, which in turn reduces the standard error and improves the efficiency of Monte Carlo simulations.

How antithetic variates work:

• For each random draw, generate its antithetic counterpart (e.g., if using standard normal variables, for each draw Z, use -Z as the antithetic)
• Run two simulations: one with original draws, one with antithetic draws
• Average the results from both simulations
• The negative correlation between the two sets of results reduces the overall variance

This technique is particularly useful in Monte Carlo simulations for option pricing, risk measurement, and other financial applications where variance reduction is important for computational efficiency.