#### Executive summary

The Monte Carlo Simulation is a technique used to stimulate potential changes to a value, a price, or any number, usually over a number of time periods. It has a wide variety of applications, some of which include: stock prices and inflation rates.

#### Key learning objectives:

- What is the Monte Carlo Simulation?
- What are some of its uses in financial markets?
- How does the simulation work in practice?

#### What is the Monte Carlo Simulation?

- A method used to stimulate a unique path for potential changes to a number
- Based on a random pick from an assumed probability distributed with a mean and standard deviation
- When repeated numerous times it defines the probability distribution of the final outcomes

#### Under which conditions can the simulation be used?

Essentially it can be used in any area where numbers are subject to change, but where the change is not perfectly predictable, or is subject to some randomness in its movement.#### What are some of its uses in financial markets?

- Valuation of certain types of options
- Potential changes to the price of assets over time
- In the measurement and management of risk

#### What does the Monte Carlo method require?

- An average for the expected change
- A standard deviation/volatility

#### How does the simulation work in practice?

- Today’s value = 100. We want to know what the number could potentially be tomorrow: let's assume that tomorrow we expect the number to remain unchanged, but subject to some variability. Assume that it could be any of the numbers in the figure below - The probabilities associated with those numbers are also shown:
- As shown in the graphic above, take 100 pieces of paper, and write one outcome on each piece reflecting the probabilities of each outcome. Put them all in a bucket, and pick one at random. This will give you the next potential measurement. Every time you take a random pick, you’ll get a different outcome, hence reflecting the nature of the distribution
- As to where the averages and probabilities come from, we can get the distribution of prices from historic data, or make rational assumptions about them
- We can repeat this as many times as needed, and hence generate a simulated path for changes to the original number