Monte Carlo Simulation: A Beginner’s Guide | CFA Level I Quantitative Methods

Today, we’ll take a whirlwind tour of Monte Carlo simulation. This complex topic can be overwhelming, but we’ll cover the essentials so you can appreciate its applications in finance. Let’s dive in!

Understanding Monte Carlo Simulation

Monte Carlo simulation is a computer-based technique where probability distributions play a vital role. Let’s illustrate this with an example of evaluating the price movements of a stock option:

1. Define the quantity of interest: In our case, it’s the option value in terms of underlying variables. We’ll determine the option value as a function of the stock price and interest rate.
2. Specify a time horizon: Split the time horizon into sub-periods. For simplicity, we’ll use four time periods, but real-world simulations often involve many more.
3. Choose models and assumptions: These drive the underlying variables and can be in the form of probability distributions.
4. Generate random numbers: A computer program generates random numbers for each model, calculates the underlying variables, and passes the outcomes to the function to determine the expected stock option value. Repeat this process for each time period.
5. Iterate: Perform the entire process multiple times, generating different sequences of outcomes. Modern computers can handle thousands to millions of iterations.
6. Analyze the results: Collate the outcomes, extract meaningful statistics (mean, standard deviation, etc.), and analyze the distribution characteristics.

Monte Carlo simulation has various applications in finance, such as:

• Valuing complex securities
• Evaluating trading strategies
• Calculating value at risk estimates
• Simulating pension fund assets and liabilities
• Valuing assets with non-normal returns distribution

Limitations of Monte Carlo Simulations

Despite its versatility, Monte Carlo simulation has its drawbacks:

• Complexity: Modelling can be intricate and challenging.
• Dependency on models and assumptions: Inaccurate models or assumptions can yield flawed results.
• Lack of analytical insights: As a statistical tool, it can’t provide insights that analytical tools can.

Historical Simulation: An Alternative Approach

Historical simulation is similar to Monte Carlo simulation but uses historical data instead of random number generators and analyst-determined models. This method has its pros and cons:

• Advantage: Results directly reflect frequencies in the historical data, providing actual distributions rather than analyst-modeled ones.
• Disadvantage: It’s unable to perform “what if” analysis like Monte Carlo simulation and is restricted to scenarios based on historical data.