[其它考试]金融风险管理师FRM2012考试真题.doc

Question bank Monte Carlo Methods Let N be an n x 1 vector of independent draws from a standard normal distribution, and let V be a covariance matrix of market time-series data. Then, if L is a diagonal matrix of the eigenvalues of V, E is a matrix of the eigenvectors of V, and CC is the Cholesky factorization of V, which of the following would generate a normally distributed random vector with mean zero and covariance matrix V to be used in a Monte Carlo simulation?  TOC \o 1-3 \h \z NCCN NC E LE Cannot be determined from data given Consider a stock that pays no dividends, has a volatility of 25% pa and an expected return of 13% pa. The current stock price is S0 = $30. This implies the model St+1 = St(1 + 0.13 At + 0.25yAt e), where e is a standard normal random variable. To implement this simulation, you generate a path of the stock price by starting at t = 0, generating a sample for e, 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 for e will implement this simulation properly? Generate a sample for e by using the inverse of the standard normal cumulative distribution of a sample value drawn from a uniform distribution between 0 and 1. Generate a sample for e by sampling from a normal distribution with mean 0.13 and standard deviation 0.25. Generate a sample for e 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. Generate a sample for e 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. Continuing with the previous question, you have implemented the simulation process discussed above using a time