Monte Carlo Analysis

Inputs

Identify variables

r

These are the most important variables I want to study.

Have an effect on output

Have known probability distributions

r

I must be able to guess or know, with some degree of accuracy, the distribution of the uncertainty in the input variables.This point cannot be stressed enough. If I have no idea what the distribution function of the inputs is, the whole analysis is useless.Sometimes it is better not to pick the obvious input (if we know nothing about its distribution), but some other driver for which we have a better estimate of its distribution.Assuming a normal distribution without convincing ourselves it makes sense (can the variable have positive and negative values? is the distribution likely symmetric? ...) is a sure recipe for disaster.

Standard Deviation

Number of variables

r

Be very wary of the "curse of dimensionality". Models become intractable very quickly when as we add inputs to our analysis.

Number should be restricted (to relevant variables only)

Large number of variables can distort the outcome

Relationship between variables

Independence

Independence is not transitive among variables

Uncorrelateness does not always imply independence

Correlation

Must be stable

Assumed as intrinsic characteristic of the distribution

Reasons to choose

We know something about the distribution

We want to determine required operational margins

There are differences of opinion concerning that input

We want to price the risk associated with it

It is "systematic"

It is of concern to some actors, but not others

It is under our control

Excel Techniques

Put all inputs in the same worksheet as the outputs

How to simulate ANY probability distribution

1. Draw from a [0,1] uniform

2. This picks a point in the cumulative distribution function (cdf)

3. Use the inverse of the cdf to find what variable value corresponds with that point

Voilà

Outputs

r

What is it that we are interested in knowing the distribution of?

Understand shape of uncertainty

Graphics

Summaries