Forecast Future Values of an Asset based on Volatility and Drift

Purpose

This calculator simulates one future value path for an asset using drift and volatility inputs.

It is useful for quick scenario exploration when you want a stochastic (randomized) path rather than a fixed deterministic curve.

Background

Drift-volatility path simulation

The path uses multiplicative random returns of the form:

$$R_t=\exp(\mu+\sigma Z_t)$$

where $\mu$ is Drift, $\sigma$ is Volatility, and $Z_t$ is a standard normal random draw.

Inputs

• starting_price: Initial asset value used as the first plotted point.
• periods: Number of simulated points in the returned series.
• volatility: Dispersion factor of the random return term.
• drift: Mean-growth component applied inside the exponential return term.

Results

• Forecast Values: One simulated value path as a list.
• Forecast chart: Line chart of the simulated path versus forecast step index.

Understanding the Calculation

1. qCalc generates periods random multiplicative returns:

$$R_t=\exp(\text{drift}+\text{volatility}\times Z_t)$$

2. The path starts with starting_price.

3. For each next step, the previous price is multiplied by the generated return for that step index.

4. The output path is charted as Forecast Value Path.

Example

Example scenario:

• starting_price 100
• periods 10
• volatility 0.05
• drift 0.0

Expected interpretation:

• The first value is the starting price.
• Later values move up or down depending on random draws, with larger swings when volatility is higher.

Important Assumptions and Interpretation

• This function produces a single random path per run. Running again with the same inputs generally gives different values.
• No random seed input is provided in this calculator, so results are not fixed/reproducible by default.
• The model is a simplified stochastic path generator for exploration, not a calibrated market model.
• The returned list length follows the periods setting; when periods is 1, the path contains only the starting value.