Module 6.1: Lognormal Distributions and Simulation Techniques

Question 1

what is a lognormal distribution

Answer 1

comes from taking a normal distribution and usinge(about 2.718) raised to the power of each value. This means if you take the natural log (ln) of a lognormal distribution, you get back to a normal distribution - that’s why it’s called “lognormal”

Question 2

What is a lognormal distribution useful for

Answer 2

We use natural logs to calculate continuous compounding returns. The lognormal distr is useful for modeling asset prices if we think it’s an asset’s future price as the result of a continuously compounding return on it’s current price.

Asset prices can’t go below zero (you can’t have negative stock prices)

Question 3

Describe Monte Carlo simulation

Answer 3

For each of the risk factors, the analyst must specify the parameters of the probability distribution that the risk factor is assumed to follow. A computer is then used to generate random values for each risk factor based on its assumed probability distributions. Each set of randomly generated risk factors is used with a pricing model to value the security.

This procedure is repeated many times (100s, 1,000s, or 10,000s), and the distribution of simulated asset values is used to draw inferences about the expected (mean) value of the security—and possibly the variance of security values about the mean as well.

Question 4

What is monte carlo useful for? What are some of the pros and cons?

Answer 4

Monte carlo is used to
- value complex securities
- simulate profits / lossess froma. trading strat
- Calculate estimates of value at risk (VaR) to determine the riskiness of a portfolio of assets and liabilities.
- Simulate pension fund assets and liabilities over time to examine the variability of the difference between the two.
- Value portfolios of assets that have nonnormal return distributions.

MC advantage
- inputs not limited to historical data
- analysts can test scenarios that haven’t occurred yet

MC limitations:
- fairly complex and won’t provide answers taht are better than the assumptions about hte distributions of the risk factors and the pricing valuation model that is used
- it’s a statistical method and NOT an analytical one

Question 5

What is Resampling

Answer 5

is a way to generate data for simulations when we don’t have complete population data. We take our existing sample data and create multiple new samples from it to estimate key statistics like averages and risk measures.

When resampling is done, the subsamples that are repeatedly drawn from the original observed samples will REMAIN THE SAME

Question 6

bootstrap resampling

Answer 6

we draw repeated samples of sizenfrom the full dataset, replacing the sampled observations each time so that they might be redrawn in another sample. We can then directly calculate the standard deviation of these sample means as our estimate of the standard error of the sample mean.

Question 7

What are some features of the Monte Carlo simulation

Answer 7

• generates a RANGE of values and not one single value
• useful for return and risk analysis
• useful for complex securities within no analytical formula for pricing
• model assumptions can be changed to assess sensitivity of output