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.