# monte carlo

Bounded random walk simulation that projects the distribution of possible price paths for a prediction market.

## How It Works

1. **Starting point**: Current market price
2. **Simulation**: Runs N random walks (configurable, default 1,000)
3. **Each walk**: Steps forward in time with random price changes drawn from a calibrated distribution
4. **Bounds**: Prices are bounded between 0% and 100% (prediction market constraints)
5. **Output**: Distribution of final prices across all simulations

```
For each simulation:
  price = current_price
  for each time step:
    price += drift + volatility * random_normal()
    price = clamp(price, 0.01, 0.99)
  record final price
```

## Parameters

| Parameter       | Default                        | Configurable | Description                                  |
| --------------- | ------------------------------ | ------------ | -------------------------------------------- |
| **Simulations** | 1,000                          | Yes          | Number of random walks to run                |
| **Volatility**  | Estimated from historical data | Yes          | Standard deviation of price changes per step |
| **Drift**       | Based on momentum signals      | Yes          | Directional bias per step                    |
| **Time steps**  | Based on days to resolution    | Auto         | How many steps to simulate                   |

## Reading the Output

The Monte Carlo output shows:

* **Histogram**: Distribution of simulated final prices
* **Median outcome**: The 50th percentile price
* **Confidence interval**: Typically 10th to 90th percentile range
* **Probability above/below current**: What percentage of simulations end higher or lower than the current price

## Interpretation

| Result                      | Meaning                                   |
| --------------------------- | ----------------------------------------- |
| **Tight distribution**      | Market is stable, low volatility expected |
| **Wide distribution**       | High uncertainty, many possible outcomes  |
| **Skewed distribution**     | Asymmetric risk (more upside or downside) |
| **Median far from current** | Drift suggests the market may move        |

## Limitations

* Random walk assumes future price changes are independent of past changes. In reality, prediction markets can trend.
* Volatility is estimated from historical data, which may not reflect future conditions.
* Near-resolution markets converge toward 0% or 100%, which the bounded model captures but the drift estimates may lag.

## Calibration

Adjust Monte Carlo parameters in the [Calibrate tab](file:///6948179/calibration/parameters.md):

* Number of simulations
* Volatility multiplier
* Drift sensitivity


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