> For the complete documentation index, see [llms.txt](https://manic.gitbook.io/manic.trade-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://manic.gitbook.io/manic.trade-docs/markets/stake-shares-and-premium.md).

# Stake, Shares, and digitalPrice

When users open a position, they are effectively holding $$x = \frac{\text{Stake}}{\text{digitalPrice}}$$ shares, and the payout is $$x \times \text{PayoutRate}$$.

`digitalPrice` is the fair value of a position — the model's estimate of the probability that the market moves in the predicted direction by expiry. It is a value between 0 and 1. For example, a `digitalPrice` of 0.25 means the model estimates a 25% chance the trade wins.

In practice, `digitalPrice` is influenced by:

* $$t\_1$$ : time to maturity. More time → higher probability of crossing a boundary → higher `digitalPrice`.
* $$\sigma$$ : implied price volatility. Higher volatility → wider expected price range → `digitalPrice` shifts depending on where the boundary is set.
* $$r$$ : interest rate risk, which does not quite exist in crypto.
* $$K$$ : the target price boundary at time $$t\_0$$. The further $$K$$ is from $$P\_0$$, the lower the probability of crossing it → lower `digitalPrice`.
* $$P\_0$$ : the current ($$t\_0$$) price when opening the position.

On Manic, the instant creation and settlement of positions give users little exposure to time value risk, so `digitalPrice` mainly reflects volatility and the distance of $$K$$ from $$P\_0$$.

If the user opens a HIGHER position, `digitalPrice` is:

$$
\text{digitalPrice}(P\_0, t\_1) = P\_0 , N(d\_1) - K e^{-r t\_1} N(d\_2)
$$

If the user opens a LOWER position, `digitalPrice` is:

$$
\text{digitalPrice}(P\_0, t\_1) = K e^{-r t\_1} N(-d\_2) - P\_0 , N(-d\_1)
$$

where the intermediate variables $$d\_1$$ and $$d\_2$$ are:

$$
d\_1 = \frac{\ln\left(\frac{P\_0}{K}\right) + \left(r + \frac{\sigma^2}{2}\right) t\_1}{\sigma \sqrt{t\_1}}
$$

$$
d\_2 = d\_1 - \sigma \sqrt{t\_1}
$$

$$N(\cdot)$$ is the cumulative distribution function of the standard normal distribution.

As volatility $$\sigma$$ is not a stable parameter, `digitalPrice` is dynamically calculated and changes over time.

## Multipliers

The Multiplier a user receives is directly derived from `digitalPrice`:

$$
\text{Multiplier} = \frac{1}{\text{digitalPrice}}
$$

Setting a higher multiplier means placing $$K$$ further from $$P\_0$$. This lowers the probability of crossing the boundary, which lowers `digitalPrice`, which in turn raises the Multiplier. The stake amount does not change — what changes is how many shares that stake buys.

Higher multipliers represent lower-probability outcomes. Users should expect to win less frequently, but each win yields a proportionally larger payout.