NO.PZ2023091601000099
问题如下：
A risk manager at a hedge fund wants to
conduct a simulation to forecast the stock price of a particular company at a
future date. The manager aims to achieve this by simulating the values of a
European option and an Asian option on the company’s stock that mature on the
specified future date, and considers several methods to improve the accuracy of
the simulation. Which of the following statements is correct regarding the
methods typically used to reduce sampling error?
选项：
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.
解释：
D 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.
老师，C和D 能否翻译一下？不明白C的closed form是啥意思，C为啥不对？
对偶变量是和抽取的变量相关系数相反的
那控制变量呢？
