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Answer: The application of control variates involves employing a variable with a mean of zero and a strong positive correlation with the simulated values
ExplanationD is correct. This is the definition of control variates. A is incorrect. Antithetic variables have to be negatively correlated to the simulation variables in order to reduce the Monte Carlo sampling variability for a given number of replications, or to reduce the number of replications while retaining the current level of sampling variability. B is incorrect. Both techniques can be used simultaneously, and the purpose of the two techniques is to reduce Monte Carlo sampling error - not bootstrapping error. C is incorrect. In the first place, Monte Carlo simulation is evidently most useful when no analytical or closed-form solution exists -for example, when pricing complex exotic options. Hence, using control variates to reduce sampling error in Monte Carlo simulation would consequently be helpful in cases where no analytical solution exists.
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A hedge fund's risk manager intends to conduct a simulation to forecast the future stock price of a particular company. This involves simulating future values for both a European option and an Asian option on the company's stock, with both options set to expire on the same future date. The manager is also exploring different methodologies to improve the accuracy of the simulation. Which of the following statements correctly describes the standard techniques employed to reduce sampling error?
A
Antithetic variables introduce a set of random variables that are positively correlated with the simulation variables to reduce the number of replications.
B
Control variates and antithetic variables both reduce bootstrapping sampling variability for a given number of replications.
C
The use of control variates is limited to simulations in which there is a closed-form solution with which to compare the simulated outcome.
D
The application of control variates involves employing a variable with a mean of zero and a strong positive correlation with the simulated values
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