🎲 What Is Monte Carlo Simulation?
Monte Carlo Simulation is a statistical technique used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables.
In simple terms, it’s a way to estimate risk and uncertainty by simulating thousands (or millions) of possible scenarios.
🧠 How It Works (Step by Step)
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Define the problem — e.g., you’re trying to forecast the future value of a portfolio, a project’s cash flow, or the price of a stock.
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Identify uncertain variables — like market return, interest rates, or costs.
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Assign a probability distribution to each uncertain variable (normal, uniform, etc.).
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Run simulations — a computer generates random values for each variable thousands of times, calculates the result each time, and stores them.
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Analyze the outcomes — you get a probability distribution of possible results, not just a single forecast.
📈 Where It’s Used
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Finance: Portfolio risk analysis, value-at-risk (VaR), option pricing
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Project Management: Budget forecasting and completion time estimation
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Engineering & Manufacturing: Quality control, reliability assessment
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Energy & Environment: Oil pricing, climate modeling
🔢 Example (Finance)
Suppose you’re forecasting the future value of a $100,000 investment over 1 year.
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Expected return: 8%
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Standard deviation: 15%
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Run 10,000 simulations, randomly sampling from a normal distribution.
You’ll get a bell curve showing:
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The mean projected value (say, ~$108,000),
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The range of outcomes (say, $70K–$140K),
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The probability of losing money (e.g., 10%).
✅ Why Use It?
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Captures uncertainty and volatility
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Provides probabilistic outcomes, not just averages
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Helps in better decision-making under risk
