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Explanation:
The antithetic variate technique reduces Monte Carlo sampling error by rerunning the simulation using a complement set of the original set of random variables. If the original set of random draws is denoted for each replication, then the simulation is rerun with the complement set of random numbers denoted .
(Book 2, Module 24.1, LO 24.c)
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Question 50
A risk manager is conducting a Monte Carlo simulation by generating random values from a standard normal probability distribution. He is interested in reducing Monte Carlo sampling error and knows that increasing the number of scenarios will improve the accuracy of this simulation. However, he is also aware that increasing the number of scenarios can become costly for complex simulations. As a result, the manager is researching variance reduction techniques as an alternative way to reduce sampling error. Which of the following statements best explains the implementation of the antithetic variate technique? Monte Carlo sampling error is reduced by:
A
replacing a simulated variable that has unknown properties with a similar variable that has known properties.
B
reusing the same set of standard normal random variables for each simulation run while testing with different Dickey–Fuller (DF) parameters.
C
splitting a longer time series into shorter time frames, such that a six-month time series of data can be subdivided into three sets of two-month experiments.
D
rerunning the simulation using a complement set of random numbers, such that the complement set of values may be a negative value of the original random number drawn.