NO.PZ2023091601000092
问题如下：
Consider a stock that pays no
dividends, has a volatility of 25% per annum and an expected return of 13% per
annum. Suppose that the current share price of the stock, S0, is USD 30. You
decide to model the stock price behavior using a discrete-time version of geometric
Brownian motion and to simulate paths of the stock price using Monte Carlo
simulation. Let Δt denote the time interval used and let St denote the stock
price at time interval t. So, according to your model,
, whereεis a standard
normal variable.
To implement this
simulation, you generate a path of the stock price by starting at t = 0,
generating a sample for ε updating the stock price according to the model,
incrementing t by 1, and repeating this process until the end of the horizon is
reached. Which of the following strategies for generating a sample forεwill implement
this simulation properly?
选项：
A.
Generate a sample
for ε by using the inverse of the standard normal cumulative distribution of a
sample value drawn from a uniform distribution between 0 and 1.
B.
Generate a sample
for ε by sampling from a normal distribution with mean 0.13 and standard
deviation 0.25.
C.
Generate a sample
for ε by using the inverse of the standard normal cumulative distribution of a
sample value drawn from a uniform distribution between 0 and 1. Use Cholesky
decomposition to correlate this sample with the sample from the previous time
interval.
D.
Generate a sample
for ε by sampling from a normal distribution with mean 0.13 and standard
deviation 0.25. Use Cholesky decomposition to correlate this sample with the
sample from the previous time interval.
解释：
Monte Carlo
Simulation assumes independence across time so there is no need to correlate
samples from time period to time period, eliminating c and d. Choice a
describes a valid method for generating a sample from a standard normal
distribution.
面一道题目中关于“Correlations among variables can be incorporated into a Monte Carlo simulation.“的表述是正确的，为什么这道题“Use Cholesky decomposition to correlate this sample with the sample from the previous time interval.“的表述是错误的？
