Simulation Methods

Question 1

What are two important characteristics of a lognormal distribution?

Answer 1

Bounded by zero (non-negative) and skewed to the right

Question 2

When is a random variable log-normally distributed?

Answer 2

When its natural logarithm is normally distributed.

Question 3

By which two parameters is the lognormal distribution described?

Answer 3

Mean and variance

Question 4

How to calculate the mean of a lognormal variable?

Answer 4

exp(mean + 0.5*stdev)

Question 5

How to calculate the variance of a lognormal variable?

Answer 5

exp(2mean + 0.5stdev) +

Question 6

What is a key assumption about returns for a Monte Carlo Simulation to work?

Answer 6

Returns are independently and identically distributed. The past returns don’t matter, only today

Question 7

What is resampling?

Answer 7

Repeatedly drawing samples from the original observed data sample for the statistical inference of population parameters.

Question 8

What is bootstrapping?

Answer 8

The idea behind bootstrap is to mimic the process of performing random sampling from a population to construct the sampling distribution. The difference lies in the fact that we have no knowledge of what the population looks like, except for a sample with size n drawn from the population. Because a random sample offers a good representation of the population, we can simulate sampling from the population by sampling from the observed sample. In other words, the bootstrap mimics the process by treating the randomly drawn sample as if it were the population.

Question 9

What are two strengths and one weakness of bootstrapping?

Answer 9

Simple to perform
Offers good representation of the statistical features of the population.

Bootstrapping only provides statistical estimates, not results